Experiment 2

Load Raw Data

These data were collected in a two-alternative forced choice experiement where participants judged stimuli at varying levels of evidence and were either correct or incorrect on each trial. In experiment 2, each participant was assigned to one of three possible uncertainty visualization conditions: regular HOPs, fast HOPs, or line ensembles.

# e1df = read.csv("E1-AnonymousRawData-InferenceSample.csv")
e2df = read.csv("E2-AnonymousRawData.csv")

Preprocessing

Reformat the raw data from the experiment as a list, changing types to integers as needed and taking the absolute value of ratio (i.e., stimulus intensity). This step will enable Stan to correctly process the data.

# prepare data for model
useData <-data_frame(
  "correct" = as.integer(e2df$Correct),
  "intensity" = abs(e2df$Ratio),
 "condition" = as.factor(e2df$Visualization),
 "subject" = as.factor(as.integer(as.factor(e2df$WorkerID)))
)

Model Specification

Our statistical model is a variation on Bayesian hierarchical probit regression.

We model the probability of a correct response from 0.5 (guessing) to 1 - lapse rate (the maximum estimated performance for each participant) as a function of stimulus intensity using a scaled and shifted cumulative normal distribution. This is called the psychometric function, and it will be used as the inverse link function in our regression model. Here are the parameters of the psychometric function:

  • threshold: mean of the cumulative Gaussian in stimulus intensity units,
  • spread: standard deviation (sd) of the cumulative Gaussian in stimulus intensity units,
  • guess rate: the lower bound of the cumulative probability density which is .5 for a two alternative forced choice task with equally likely alternatives
  • lapse rate: the rate of error for an individual due to lapses of attention which are independent of the stimulus

We define the psychometric function in R so that we can use it in postprocessing.

psychometric <- function(intensity,m,sd,guess,lapse){
  # handle arguments
  if(missing(guess)) {
    guess <- .5
  }
  if( missing(lapse)) {
    lapse <- 0
  }
  intensity <- as.matrix(intensity)

  # set upper and lower bounds
  lowerBound <- guess
  upperBound <- 1 - lapse

  # calculate z score for each level of intensity
  r <- dim(intensity)[1]
  c <- dim(intensity)[2]
  z <- (intensity - m * matrix(1, r, c)) / sd

  # scale cumulative probability density between upper and lower bound
  p <- lowerBound + pnorm(z / sqrt(2)) * (upperBound - lowerBound)
  return(p)
}

Below is the specification of the statistical model. Note the following features of the model:

  • We are modelling correctness as a binomial distributed outcome with the probability of being correct as a transformed linear model of ratio and visualization condition.
  • We use a scaled and shifted probit (the inverse of the psychometric function) as the link function for our linear model.
  • The threshold, spread, and lapse rate parameters of the model are estimated for each subject while guess rate is assumed to be .5 based on the design of the experiment.
  • We estimate the effect of each visualization condition via dummy coding.

The point of this exercise is that all parameters, both at the subject level (psychometric function parameters) and the group level (effects of visualization condition), are all estimated from raw data within one unified model.

# model specification in Stan
stanCode <-
'data {
  int<lower=0> N; // number of obs
  int<lower=0> N_subject; // number of subjects
  int<lower=0> N_condition; // number of visualization conditions
  int<lower=0,upper=1> correct[N]; // correctness of judgments on each trial
  real<lower=0> intensity[N]; // stimulus intensity on each trial
  int<lower=0> subject[N]; //subject index for each observation
  int<lower=1,upper=N_condition> condition[N_subject]; // visualization condition for each subject 
}
parameters {
  // hyperparameters for sigma of threshold, spread, and lapse
  real<lower=0> sigma_log_threshold;
  real<lower=0> sigma_log_spread;
  real<lower=0> sigma_logit_lapse;
  // effects of visualization conditions (transformed means per condition for threshold, spread, and lapse)
  vector[N_condition] b_threshold;
  vector[N_condition] b_spread;
  vector[N_condition] b_lapse;
  // for non-centered parameterization
  vector[N_subject] threshold_zoffset;
  vector[N_subject] spread_zoffset;
  vector[N_subject] lapse_zoffset;
}
transformed parameters {
  // non-centered parameterization of threshold, spread, and lapse parameters of the PF for each subject
  vector<lower=0>[N_subject] threshold;
  vector<lower=0>[N_subject] spread;
  vector<lower=0,upper=1>[N_subject] lapse;
  threshold = exp(b_threshold[condition] + threshold_zoffset*sigma_log_threshold);
  spread = exp(b_spread[condition] + spread_zoffset*sigma_log_spread);     
  lapse = inv_logit(b_lapse[condition] + lapse_zoffset*sigma_logit_lapse);
}
model {
  vector[N] p; // probability of being correct on each trial
  threshold_zoffset ~ normal(0,1); // priors for offsets per subject for non-centered parameterization of PF
  spread_zoffset ~ normal(0,1);
  lapse_zoffset ~ normal(0,1);
  sigma_log_threshold ~ cauchy(0,1); // priors for hyperparameters
  sigma_log_spread ~ cauchy(0,1);
  sigma_logit_lapse ~ gamma(2,2);
  b_threshold ~ normal(0,2); // priors for visualization effects
  b_spread ~ normal(0,2);
  b_lapse ~ normal(log(0.05/(1 - 0.05)),fabs(log(0.196/(1 - 0.196)))); // centered on logit(0.05)
  // sigma_logit_lapse ~ exponential(3);
  for (i in 1:N) {
    // psychometric function as inverse link function
    p[i] = (0.5 - lapse[subject[i]])*Phi((intensity[i] - threshold[subject[i]])/spread[subject[i]]/sqrt(2.0)) + 0.5;
  }
  correct ~ binomial(1,p);
}'

# convert to model
mdlSpec <- stan_model(model_code = stanCode)
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Core:531:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:2:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/LU:47:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:3:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Cholesky:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Jacobi:29:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:3:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Cholesky:43:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/QR:17:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Householder:27:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SVD:48:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Geometry:58:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Eigenvalues:58:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:26:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseCore:66:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:27:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/OrderingMethods:71:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseCholesky:43:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:32:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseQR:35:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:33:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/IterativeLinearSolvers:46:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
##     #pragma clang diagnostic pop
##                              ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:44:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:13: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
## static void set_zero_all_adjoints() {
##             ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:70:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:18:8: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
## size_t fft_next_good_size(size_t N) {
##        ^
## 15 warnings generated.

Next we fit the model to our data using Stan.

# run model (actually load it instead of running)
# mdl = sampling(
#   mdlSpec, 
#   data = compose_data(useData,condition = x_at_y(condition, subject),.n_name = n_prefix("N")),
#   chains = 2,
#   cores = 2,
#   warmup = 1000,
#   iter = 2000,
#   control = list(adapt_delta=0.99,max_treedepth = 15)
# )

We save the run of the model and load it, so that we don’t have to run it every time.

# saveRDS(mdl,'oneMdl.rds')
mdl <- readRDS('oneMdl.rds')

Check Model Perfomance

This kind of Bayesian model samples from a Markov Chain Monte Claro algoritm to estimate each parameter in our model. Here we can see whether the four separate simulations we ran above converged (a sign of reliable estimates) and whether the any the samples from any simulation contain autocorrelation (a sign that out simulation got stuck at a given location in parameter space, and we should run the model fit again and possibly change our model specification or priors). We check this by looking at a traceplot.

traceplot(mdl,pars=c('b_threshold[1]','b_spread[1]','b_lapse[1]','b_threshold[2]','b_spread[2]','b_lapse[2]','b_threshold[3]','b_spread[3]','b_lapse[3]','sigma_log_threshold','sigma_log_spread','sigma_logit_lapse','threshold[1]','spread[1]','lapse[1]'))

Here, we just want to see that the simulation is not getting stuck on particular parameter values.

Let’s also check whether our model had any problems identifying any of our parameters due to highly correltated parameter values. We check this using a pairs plot.

pairs(mdl,pars=c('b_threshold[1]','b_spread[1]','b_lapse[1]','b_threshold[2]','b_spread[2]','b_lapse[2]','b_threshold[3]','b_spread[3]','b_lapse[3]','sigma_log_threshold','sigma_log_spread','sigma_logit_lapse','threshold[1]','spread[1]','lapse[1]'))

Too much correlation between posterior samples would here would indicate that our model fit is probably not properly estimating these parameters due to non-identifiability.

Let’s look at the summary, paying special attention to the Rhat which should be very close to 1, and n_eff which should be within two orders of magnitude of the number of non-warmup iterations.

# get and print model summary
mdlSummary <- summary(mdl)
print(mdlSummary$summary)
##                                 mean      se_mean           sd
## sigma_log_threshold     1.083179e-01 0.0040759773  0.052589661
## sigma_log_spread        2.596112e-01 0.0043354470  0.059472580
## sigma_logit_lapse       1.974326e+00 0.0104474067  0.241475978
## b_threshold[1]          9.381986e-01 0.0012303056  0.051394479
## b_threshold[2]          8.672131e-01 0.0011278735  0.052430262
## b_threshold[3]          8.558368e-01 0.0014261445  0.062863069
## b_spread[1]             4.432826e-01 0.0022099637  0.080406625
## b_spread[2]             4.754875e-01 0.0038033414  0.085631759
## b_spread[3]             5.998302e-01 0.0037291347  0.093357858
## b_lapse[1]             -4.629199e+00 0.0181275600  0.446993037
## b_lapse[2]             -4.788735e+00 0.0235938334  0.475306032
## b_lapse[3]             -4.341325e+00 0.0211640281  0.465242575
## threshold_zoffset[1]    1.291453e-01 0.0166141443  0.998176373
## threshold_zoffset[2]    1.387799e-01 0.0162620915  0.936986437
## threshold_zoffset[3]   -1.069167e-01 0.0153426116  0.903451243
## threshold_zoffset[4]    5.297911e-02 0.0168539030  0.907713589
## threshold_zoffset[5]   -2.326056e-03 0.0175076291  0.968626186
## threshold_zoffset[6]   -3.920160e-01 0.0199157153  0.873154005
## threshold_zoffset[7]    2.311405e-01 0.0175374790  0.971636855
## threshold_zoffset[8]   -1.470438e-01 0.0182446186  0.951839170
## threshold_zoffset[9]   -4.282742e-01 0.0223752339  0.849749907
## threshold_zoffset[10]  -5.848093e-03 0.0174487255  0.978475839
## threshold_zoffset[11]   1.557685e-03 0.0174288598  0.926253353
## threshold_zoffset[12]   1.169680e-02 0.0161286940  0.921028488
## threshold_zoffset[13]  -5.651016e-02 0.0161334063  0.935462213
## threshold_zoffset[14]  -9.145528e-02 0.0170726568  0.971051074
## threshold_zoffset[15]   3.818051e-01 0.0176941840  0.985044850
## threshold_zoffset[16]  -2.721953e-01 0.0174532450  0.920676942
## threshold_zoffset[17]  -2.003886e-01 0.0166331531  0.895264290
## threshold_zoffset[18]  -5.395294e-01 0.0224147746  0.925240509
## threshold_zoffset[19]   1.211668e-02 0.0176874760  1.010957377
## threshold_zoffset[20]  -5.078965e-03 0.0159519596  0.958858403
## threshold_zoffset[21]   1.280231e-01 0.0180762827  0.959638715
## threshold_zoffset[22]  -2.024857e-01 0.0172630944  0.923877327
## threshold_zoffset[23]   3.058202e-01 0.0214975398  0.955882467
## threshold_zoffset[24]  -1.947190e-02 0.0168797657  0.986154278
## threshold_zoffset[25]   4.534405e-01 0.0228202200  1.053576182
## threshold_zoffset[26]   1.596064e-01 0.0193159601  1.009058339
## threshold_zoffset[27]   1.488109e-01 0.0149034595  0.914742398
## threshold_zoffset[28]   2.505733e-01 0.0200584645  0.989407472
## threshold_zoffset[29]   5.768787e-01 0.0243527455  0.991640337
## threshold_zoffset[30]   2.617813e-01 0.0195367538  1.030414155
## threshold_zoffset[31]  -2.080289e-01 0.0186739445  0.929657097
## threshold_zoffset[32]   1.488973e-01 0.0199065754  1.025198648
## threshold_zoffset[33]  -3.594494e-01 0.0196091669  0.940970564
## threshold_zoffset[34]  -5.251153e-02 0.0172756408  0.917320965
## threshold_zoffset[35]   1.259826e-01 0.0189249368  0.916447330
## threshold_zoffset[36]  -3.969212e-01 0.0196144838  0.931763429
## threshold_zoffset[37]   9.612675e-02 0.0205345758  1.017949766
## threshold_zoffset[38]   1.946599e-01 0.0172914479  0.941088363
## threshold_zoffset[39]  -4.374537e-01 0.0193163740  0.941993087
## threshold_zoffset[40]  -5.424103e-01 0.0205878509  0.882940331
## threshold_zoffset[41]   2.324385e-02 0.0187387146  0.908564882
## threshold_zoffset[42]   1.445721e-01 0.0171240808  0.969906509
## threshold_zoffset[43]   2.052500e-01 0.0179137176  0.956998322
## threshold_zoffset[44]  -2.781470e-01 0.0163785219  0.881479215
## threshold_zoffset[45]  -1.072034e-01 0.0172506921  0.947960280
## threshold_zoffset[46]  -1.331618e-02 0.0166041721  0.969627041
## threshold_zoffset[47]  -5.979871e-01 0.0236927946  0.957991260
## threshold_zoffset[48]  -5.731168e-01 0.0196683095  0.919344435
## threshold_zoffset[49]  -5.916742e-01 0.0201234871  0.884104824
## threshold_zoffset[50]   1.469255e-01 0.0198306363  1.049715455
## threshold_zoffset[51]   5.221296e-03 0.0196877843  0.991757422
## threshold_zoffset[52]   2.632039e-01 0.0183990522  1.005245882
## threshold_zoffset[53]  -4.605234e-01 0.0239848480  0.902870357
## threshold_zoffset[54]   2.493949e-01 0.0168321136  0.914593485
## threshold_zoffset[55]   3.097309e-01 0.0220074649  0.926089253
## threshold_zoffset[56]  -3.463109e-01 0.0198429975  0.910618470
## threshold_zoffset[57]  -4.853517e-01 0.0190496191  0.912321775
## threshold_zoffset[58]   2.326163e-01 0.0175078673  0.889921216
## threshold_zoffset[59]   5.148747e-01 0.0243106153  1.028177063
## threshold_zoffset[60]   3.430222e-01 0.0168320199  0.953004716
## threshold_zoffset[61]   3.732068e-01 0.0200248789  1.000371419
## threshold_zoffset[62]  -7.270605e-02 0.0173399920  0.951556639
## threshold_zoffset[63]   1.883492e-01 0.0175646672  0.974644898
## threshold_zoffset[64]   3.514790e-01 0.0199251700  0.957852008
## threshold_zoffset[65]  -2.486205e-01 0.0170581175  0.911338543
## threshold_zoffset[66]   5.169429e-01 0.0221617000  1.017798435
## threshold_zoffset[67]  -4.305144e-01 0.0207031443  0.907726703
## threshold_zoffset[68]   2.484263e-01 0.0203847587  0.996909105
## threshold_zoffset[69]  -4.087539e-01 0.0195388191  0.896722983
## threshold_zoffset[70]  -5.609487e-01 0.0210925021  0.916384709
## threshold_zoffset[71]   3.293143e-02 0.0164641036  0.924953859
## threshold_zoffset[72]   2.271494e-01 0.0207279055  1.012072072
## threshold_zoffset[73]   9.763396e-02 0.0178797653  0.943331273
## threshold_zoffset[74]  -1.128064e-01 0.0142583010  0.858376684
## threshold_zoffset[75]   1.761938e-01 0.0180963658  0.947889668
## threshold_zoffset[76]  -7.008710e-02 0.0178648278  0.944119865
## threshold_zoffset[77]  -8.630200e-01 0.0230310771  0.878226469
## threshold_zoffset[78]   9.942984e-02 0.0165208548  0.932787074
## threshold_zoffset[79]  -5.339056e-01 0.0231417325  0.905536048
## threshold_zoffset[80]   2.712175e-01 0.0184201604  0.972626925
## threshold_zoffset[81]  -3.247499e-01 0.0177505754  0.955810639
## threshold_zoffset[82]   2.779971e-01 0.0195294130  0.976787592
## threshold_zoffset[83]   2.290239e-01 0.0168638098  0.906490146
## threshold_zoffset[84]  -1.365546e-01 0.0178787712  0.885025086
## threshold_zoffset[85]  -4.226669e-01 0.0199981145  0.871870396
## threshold_zoffset[86]   4.311971e-02 0.0164427925  0.936429030
## threshold_zoffset[87]   1.454371e-01 0.0168066968  0.993745285
## threshold_zoffset[88]   2.033892e-01 0.0166047975  0.905666803
## threshold_zoffset[89]   2.410122e-01 0.0198546778  0.979725177
## threshold_zoffset[90]   4.751317e-01 0.0254214425  1.032186773
## threshold_zoffset[91]  -4.954947e-01 0.0205652421  0.903213874
## threshold_zoffset[92]   2.776856e-01 0.0189708269  1.016657927
## threshold_zoffset[93]   3.254236e-02 0.0179003883  0.968812139
## threshold_zoffset[94]   3.522647e-02 0.0170484701  0.995930529
## threshold_zoffset[95]   6.246901e-02 0.0192621444  0.950904308
## threshold_zoffset[96]  -1.493451e-01 0.0200777483  1.004890675
## threshold_zoffset[97]  -1.286489e-01 0.0182440302  0.985254632
## threshold_zoffset[98]  -5.395559e-01 0.0207032387  0.942006808
## threshold_zoffset[99]   2.561822e-01 0.0172500816  0.947609923
## threshold_zoffset[100]  9.974911e-02 0.0186291328  0.969476413
## threshold_zoffset[101]  5.990820e-02 0.0165920626  0.996633388
## threshold_zoffset[102] -2.163471e-01 0.0182270762  0.906309568
## threshold_zoffset[103]  4.217122e-02 0.0160533593  0.988391673
## threshold_zoffset[104] -2.519046e-01 0.0205779255  0.923268322
## threshold_zoffset[105] -6.426944e-02 0.0173653336  0.885961222
## threshold_zoffset[106]  1.920079e-01 0.0166953786  0.952407096
## threshold_zoffset[107]  1.176908e+00 0.0492978367  1.221676694
## threshold_zoffset[108] -1.542244e-01 0.0171404594  0.979143723
## threshold_zoffset[109] -7.933444e-02 0.0158388677  0.921838117
## threshold_zoffset[110]  2.121122e-01 0.0187204176  0.986134223
## threshold_zoffset[111]  1.095440e-01 0.0192051336  0.938480941
## threshold_zoffset[112]  7.443418e-02 0.0161070134  0.931180635
## threshold_zoffset[113] -3.206446e-01 0.0211207682  0.927606607
## threshold_zoffset[114] -9.196777e-02 0.0175991129  0.952065076
## threshold_zoffset[115] -2.695802e-01 0.0170795286  0.923035709
## threshold_zoffset[116]  1.810812e-02 0.0157725913  0.888855637
## threshold_zoffset[117]  2.767608e-01 0.0191553917  0.951615360
## threshold_zoffset[118]  8.321374e-02 0.0180343398  0.968773223
## threshold_zoffset[119]  3.510475e-01 0.0174752310  0.963811166
## threshold_zoffset[120] -3.142408e-02 0.0174926239  0.927741039
## threshold_zoffset[121]  5.705771e-02 0.0181373101  0.914108784
## threshold_zoffset[122] -7.171032e-02 0.0160945633  0.894552094
## threshold_zoffset[123] -3.532981e-02 0.0178381391  0.962140485
## threshold_zoffset[124]  3.240472e-01 0.0214484167  0.966640275
## threshold_zoffset[125]  3.189316e-01 0.0209343774  0.954294722
## threshold_zoffset[126]  2.350615e-01 0.0175893254  0.991142481
## threshold_zoffset[127]  3.948261e-01 0.0211599161  0.983469956
## threshold_zoffset[128] -1.018112e-01 0.0167415833  0.982564367
## threshold_zoffset[129] -5.063109e-01 0.0207361206  0.892295468
## threshold_zoffset[130]  2.716514e-01 0.0197809466  0.960524152
## threshold_zoffset[131] -4.856522e-02 0.0180888259  0.891726451
## threshold_zoffset[132]  2.258336e-01 0.0175366699  0.981796450
## threshold_zoffset[133] -1.270958e-01 0.0173744496  0.943833889
## threshold_zoffset[134]  2.935794e-01 0.0181741663  0.970417523
## threshold_zoffset[135] -9.195009e-03 0.0164024230  0.984743838
## threshold_zoffset[136]  2.985240e-01 0.0189595965  0.994957819
## threshold_zoffset[137] -1.348492e-01 0.0168748948  0.884372176
## threshold_zoffset[138]  2.256287e-01 0.0190779749  0.924883920
## threshold_zoffset[139]  4.610242e-01 0.0239978217  1.002161808
## threshold_zoffset[140] -1.369042e-01 0.0186248246  0.964755303
## threshold_zoffset[141]  3.833643e-02 0.0183821796  0.949566296
## threshold_zoffset[142]  1.976023e-01 0.0175754266  0.934709192
## threshold_zoffset[143]  1.636911e-01 0.0182836407  0.898568706
## threshold_zoffset[144]  1.780262e-01 0.0173511621  0.932766282
## threshold_zoffset[145]  2.171908e-02 0.0181189661  0.921511456
## threshold_zoffset[146]  2.756778e-01 0.0178203598  0.956295926
## threshold_zoffset[147] -9.555970e-01 0.0307562713  0.925581740
## threshold_zoffset[148]  7.811345e-02 0.0174022495  0.930734628
## threshold_zoffset[149] -4.109605e-01 0.0183309539  0.920024988
## threshold_zoffset[150] -1.390998e-01 0.0162916709  0.930569796
## spread_zoffset[1]       4.040845e-01 0.0256416257  1.044281517
## spread_zoffset[2]       4.490840e-01 0.0181800272  0.846101832
## spread_zoffset[3]       1.175208e-01 0.0157840572  0.857612550
## spread_zoffset[4]       6.188779e-01 0.0158046010  0.759206661
## spread_zoffset[5]       4.168727e-01 0.0193273716  0.904251598
## spread_zoffset[6]      -7.495005e-01 0.0159739335  0.808797438
## spread_zoffset[7]       4.968311e-01 0.0166470156  0.791261362
## spread_zoffset[8]       4.460710e-01 0.0277448329  1.046036976
## spread_zoffset[9]      -8.457427e-01 0.0151003762  0.809567032
## spread_zoffset[10]      6.970731e-01 0.0287136153  1.003933247
## spread_zoffset[11]     -7.070511e-02 0.0186155651  0.929912502
## spread_zoffset[12]     -4.314152e-01 0.0150065687  0.775725599
## spread_zoffset[13]     -4.536415e-01 0.0145232149  0.805171131
## spread_zoffset[14]     -5.578952e-02 0.0191699985  1.038267921
## spread_zoffset[15]      5.981885e-01 0.0215795295  0.936906259
## spread_zoffset[16]     -7.724797e-01 0.0150631526  0.805259195
## spread_zoffset[17]      6.885550e-02 0.0159977297  0.878275029
## spread_zoffset[18]     -5.298818e-01 0.0168291513  0.810223711
## spread_zoffset[19]      1.392026e-02 0.0194675850  1.005984815
## spread_zoffset[20]      1.949887e-02 0.0142705936  0.751592153
## spread_zoffset[21]      4.363021e-01 0.0156178242  0.747771967
## spread_zoffset[22]     -2.649252e-01 0.0152806566  0.757239309
## spread_zoffset[23]      2.683945e-01 0.0165198255  0.810507273
## spread_zoffset[24]      3.296295e-02 0.0173391314  0.999583608
## spread_zoffset[25]      7.187806e-01 0.0190612245  0.914408862
## spread_zoffset[26]      2.776720e-01 0.0227052432  1.018392603
## spread_zoffset[27]     -2.023958e-01 0.0143134550  0.727483448
## spread_zoffset[28]      5.565484e-01 0.0161043560  0.814196970
## spread_zoffset[29]      2.129071e-01 0.0167927223  0.755364717
## spread_zoffset[30]      3.349508e-01 0.0333266262  1.019457602
## spread_zoffset[31]     -5.026399e-01 0.0162207451  0.812485983
## spread_zoffset[32]      3.240571e-01 0.0281108599  1.080523255
## spread_zoffset[33]      4.011530e-01 0.0135719344  0.729066463
## spread_zoffset[34]      8.790139e-02 0.0150029712  0.802153814
## spread_zoffset[35]     -8.356861e-02 0.0142141121  0.839234183
## spread_zoffset[36]     -1.020240e-01 0.0157096847  0.790667264
## spread_zoffset[37]      4.201852e-01 0.0215601709  1.037786309
## spread_zoffset[38]      2.151625e-01 0.0140624638  0.768550968
## spread_zoffset[39]      1.246259e-01 0.0158629983  0.820949226
## spread_zoffset[40]     -7.085356e-01 0.0156346744  0.783886499
## spread_zoffset[41]     -6.650859e-02 0.0204165949  0.935347692
## spread_zoffset[42]      2.247453e-01 0.0226296472  0.993737450
## spread_zoffset[43]      3.692482e-01 0.0242232673  1.049788754
## spread_zoffset[44]     -1.244181e-01 0.0128175213  0.760508079
## spread_zoffset[45]     -3.940355e-01 0.0160715072  0.803511430
## spread_zoffset[46]     -2.477399e-02 0.0200437829  1.026715672
## spread_zoffset[47]     -1.179306e+00 0.0162680407  0.822717746
## spread_zoffset[48]     -3.286503e-01 0.0155671176  0.804143677
## spread_zoffset[49]     -5.861948e-01 0.0148951339  0.796189179
## spread_zoffset[50]      4.314825e-01 0.0177057347  0.992899689
## spread_zoffset[51]      5.362392e-01 0.0199029234  0.847628323
## spread_zoffset[52]      7.016614e-01 0.0154283457  0.780380148
## spread_zoffset[53]     -7.242438e-01 0.0165708537  0.862763252
## spread_zoffset[54]     -2.020375e-01 0.0152206228  0.792742301
## spread_zoffset[55]      6.345987e-03 0.0146175581  0.752306027
## spread_zoffset[56]     -8.054125e-01 0.0160309429  0.840451405
## spread_zoffset[57]     -6.569633e-01 0.0132762218  0.795550856
## spread_zoffset[58]     -6.615523e-01 0.0161654735  0.798095538
## spread_zoffset[59]      5.265475e-01 0.0147905738  0.731024833
## spread_zoffset[60]      4.028945e-01 0.0193997100  0.920241899
## spread_zoffset[61]      2.908079e-01 0.0155245155  0.728660257
## spread_zoffset[62]     -4.222582e-01 0.0176939034  0.937276562
## spread_zoffset[63]      5.327210e-01 0.0181095265  0.840530326
## spread_zoffset[64]      6.496609e-01 0.0188342254  0.827378019
## spread_zoffset[65]      6.017323e-01 0.0124073264  0.716953335
## spread_zoffset[66]      3.272521e-01 0.0174693428  0.800467863
## spread_zoffset[67]     -6.436348e-01 0.0142975884  0.799945017
## spread_zoffset[68]      1.031541e-01 0.0242189375  0.998207728
## spread_zoffset[69]     -1.364609e+00 0.0168300951  0.815109278
## spread_zoffset[70]      1.178042e-02 0.0165659083  0.841973497
## spread_zoffset[71]      5.305795e-01 0.0191113392  0.866057786
## spread_zoffset[72]      3.553164e-01 0.0185831445  0.975360557
## spread_zoffset[73]      5.174700e-02 0.0170713673  0.885635803
## spread_zoffset[74]      1.164035e-02 0.0164387515  0.797363092
## spread_zoffset[75]      2.731711e-01 0.0122642664  0.737691019
## spread_zoffset[76]      1.436561e-02 0.0213188406  0.955172294
## spread_zoffset[77]     -1.689875e+00 0.0225882365  0.846049983
## spread_zoffset[78]     -3.546576e-01 0.0139561623  0.762443921
## spread_zoffset[79]      2.347579e-01 0.0146836689  0.814924426
## spread_zoffset[80]      2.398022e-01 0.0206647096  0.921124376
## spread_zoffset[81]      1.244355e-01 0.0165680715  0.867337975
## spread_zoffset[82]      4.812325e-01 0.0175100567  0.780999685
## spread_zoffset[83]     -1.751925e-01 0.0153899824  0.794977982
## spread_zoffset[84]     -9.208259e-01 0.0158711176  0.834646782
## spread_zoffset[85]     -1.020572e+00 0.0162312504  0.844499759
## spread_zoffset[86]     -3.181043e-01 0.0292752120  1.013439115
## spread_zoffset[87]      2.174256e-01 0.0285458490  1.116235482
## spread_zoffset[88]      3.330073e-01 0.0162522929  0.778813209
## spread_zoffset[89]      3.784042e-01 0.0222692847  0.950514502
## spread_zoffset[90]      9.394269e-01 0.0179376799  0.823496538
## spread_zoffset[91]     -6.662734e-01 0.0135925297  0.806245843
## spread_zoffset[92]      3.226376e-01 0.0162038199  0.773785968
## spread_zoffset[93]      3.975983e-01 0.0296515746  1.016513855
## spread_zoffset[94]      4.738809e-02 0.0215007484  1.016795381
## spread_zoffset[95]      2.424367e-01 0.0153583626  0.764831868
## spread_zoffset[96]      7.789003e-02 0.0369108292  1.125148468
## spread_zoffset[97]      1.574749e-01 0.0184211056  1.057006075
## spread_zoffset[98]     -9.762846e-01 0.0196220165  0.852786997
## spread_zoffset[99]      6.153656e-01 0.0172188258  0.800509954
## spread_zoffset[100]     3.257359e-01 0.0148356032  0.746088224
## spread_zoffset[101]     9.852179e-01 0.0228124226  0.928978797
## spread_zoffset[102]    -3.062543e-01 0.0140868977  0.776869407
## spread_zoffset[103]     1.537346e-01 0.0192063741  1.032597706
## spread_zoffset[104]    -1.969986e-01 0.0155580943  0.819615622
## spread_zoffset[105]     1.733508e-02 0.0175474864  0.814227583
## spread_zoffset[106]     5.092781e-01 0.0177444109  0.858870787
## spread_zoffset[107]     7.652216e-01 0.0287543120  0.869894006
## spread_zoffset[108]     5.808476e-02 0.0172966663  0.786637922
## spread_zoffset[109]    -3.307785e-02 0.0135835498  0.772353292
## spread_zoffset[110]     4.558518e-01 0.0308045363  1.042134767
## spread_zoffset[111]    -2.519096e-01 0.0164127608  0.760796541
## spread_zoffset[112]    -2.401141e-01 0.0155102460  0.779341621
## spread_zoffset[113]    -4.414138e-01 0.0162225033  0.802913085
## spread_zoffset[114]     3.127212e-01 0.0297503334  1.053184057
## spread_zoffset[115]    -5.698434e-02 0.0148729402  0.783580783
## spread_zoffset[116]    -2.633166e-01 0.0151088776  0.812026184
## spread_zoffset[117]     2.827028e-01 0.0193763956  0.867598941
## spread_zoffset[118]     2.196846e-01 0.0231055330  1.039378889
## spread_zoffset[119]    -3.335949e-01 0.0147207696  0.760809709
## spread_zoffset[120]     6.357032e-01 0.0142736374  0.727162882
## spread_zoffset[121]    -3.004599e-01 0.0157453621  0.751348138
## spread_zoffset[122]    -7.894109e-01 0.0125800936  0.757208732
## spread_zoffset[123]    -2.679996e-01 0.0133534015  0.765352328
## spread_zoffset[124]     3.234768e-01 0.0142029278  0.740325467
## spread_zoffset[125]     1.808265e-02 0.0142268956  0.725270106
## spread_zoffset[126]     2.649743e-01 0.0249858493  0.987567229
## spread_zoffset[127]     6.096536e-01 0.0180314903  0.860949652
## spread_zoffset[128]    -2.202442e-01 0.0230209885  1.013111688
## spread_zoffset[129]    -6.997819e-01 0.0135907413  0.813008496
## spread_zoffset[130]     5.799320e-01 0.0165391583  0.775864817
## spread_zoffset[131]    -5.898301e-01 0.0142926592  0.783484167
## spread_zoffset[132]     3.481504e-01 0.0269385465  1.044860069
## spread_zoffset[133]    -4.002112e-01 0.0149020712  0.801038819
## spread_zoffset[134]     2.904461e-01 0.0149826413  0.746172806
## spread_zoffset[135]    -7.894409e-02 0.0189024825  0.983451790
## spread_zoffset[136]     8.059051e-01 0.0158186105  0.752138708
## spread_zoffset[137]    -3.956006e-01 0.0137384757  0.792649959
## spread_zoffset[138]    -1.465901e-01 0.0152461440  0.753929423
## spread_zoffset[139]     3.258611e-01 0.0169824491  0.752093620
## spread_zoffset[140]    -5.928110e-01 0.0138296325  0.794400246
## spread_zoffset[141]     4.492808e-01 0.0186174120  0.838085221
## spread_zoffset[142]    -2.033806e-01 0.0260867159  1.079531605
## spread_zoffset[143]    -3.805748e-01 0.0144172994  0.807284710
## spread_zoffset[144]     1.471646e-01 0.0150411220  0.806880638
## spread_zoffset[145]     2.540874e-01 0.0264194905  1.061089894
## spread_zoffset[146]     1.353883e-01 0.0231292095  0.963298934
## spread_zoffset[147]    -1.417668e+00 0.0159614921  0.887898121
## spread_zoffset[148]     2.693586e-01 0.0238552708  0.999499567
## spread_zoffset[149]    -4.244872e-01 0.0150394978  0.724049194
## spread_zoffset[150]    -4.445115e-01 0.0167352714  0.775049593
## lapse_zoffset[1]        1.193495e+00 0.0142892238  0.373781320
## lapse_zoffset[2]       -8.410605e-02 0.0210131502  0.832119935
## lapse_zoffset[3]        1.174912e-01 0.0196010306  0.681507224
## lapse_zoffset[4]       -3.890512e-01 0.0158455987  0.749046378
## lapse_zoffset[5]        1.178403e-01 0.0224103077  0.697628265
## lapse_zoffset[6]       -5.646686e-01 0.0156335548  0.741370613
## lapse_zoffset[7]       -1.895730e-01 0.0206763447  0.814947778
## lapse_zoffset[8]        4.339784e-01 0.0275308938  0.660942834
## lapse_zoffset[9]       -6.394117e-01 0.0145240442  0.726111875
## lapse_zoffset[10]       6.536631e-01 0.0318662197  0.709123757
## lapse_zoffset[11]       2.212155e-01 0.0198070678  0.699168946
## lapse_zoffset[12]      -5.876531e-01 0.0160216629  0.702275479
## lapse_zoffset[13]      -6.128570e-01 0.0151484596  0.695937184
## lapse_zoffset[14]       1.404611e+00 0.0097379698  0.253378762
## lapse_zoffset[15]       3.017964e-01 0.0287199999  0.796429399
## lapse_zoffset[16]      -7.298381e-01 0.0147609614  0.732166908
## lapse_zoffset[17]      -2.508128e-01 0.0174453686  0.756888475
## lapse_zoffset[18]      -6.041101e-01 0.0165033216  0.730216766
## lapse_zoffset[19]       1.940475e+00 0.0127724103  0.259022110
## lapse_zoffset[20]      -5.369452e-01 0.0150764446  0.765743857
## lapse_zoffset[21]      -3.927495e-01 0.0172735051  0.751833576
## lapse_zoffset[22]      -6.780606e-01 0.0151274677  0.708176187
## lapse_zoffset[23]      -2.067841e-01 0.0202908518  0.811848090
## lapse_zoffset[24]       2.109710e+00 0.0130146854  0.264188788
## lapse_zoffset[25]       3.337155e-01 0.0239142195  0.749801477
## lapse_zoffset[26]       3.656762e-01 0.0271766971  0.684929068
## lapse_zoffset[27]      -5.675058e-01 0.0167978400  0.741904596
## lapse_zoffset[28]      -1.028011e-01 0.0186897570  0.770488045
## lapse_zoffset[29]      -4.224066e-01 0.0153732074  0.755901189
## lapse_zoffset[30]       9.382733e-01 0.0233042964  0.471805580
## lapse_zoffset[31]      -5.547477e-01 0.0181984886  0.756462343
## lapse_zoffset[32]       1.192735e+00 0.0165271509  0.394109166
## lapse_zoffset[33]      -4.541349e-01 0.0162255288  0.781556364
## lapse_zoffset[34]      -3.692591e-01 0.0159848712  0.760227214
## lapse_zoffset[35]      -3.863123e-01 0.0163778590  0.752502352
## lapse_zoffset[36]      -5.176015e-01 0.0155422096  0.765309663
## lapse_zoffset[37]       1.390523e+00 0.0129352425  0.341070460
## lapse_zoffset[38]      -3.963935e-01 0.0170403540  0.797974200
## lapse_zoffset[39]      -5.043856e-01 0.0164204833  0.690860074
## lapse_zoffset[40]      -6.714085e-01 0.0153478052  0.695456281
## lapse_zoffset[41]      -3.770979e-02 0.0204641524  0.744905088
## lapse_zoffset[42]       1.511241e+00 0.0100391195  0.248684526
## lapse_zoffset[43]       5.977596e-01 0.0252808074  0.706724327
## lapse_zoffset[44]      -4.838180e-01 0.0150364289  0.772844047
## lapse_zoffset[45]      -5.938989e-01 0.0154527984  0.715646812
## lapse_zoffset[46]       2.069608e+00 0.0132133444  0.265048137
## lapse_zoffset[47]      -7.583074e-01 0.0154572050  0.686514487
## lapse_zoffset[48]      -5.986918e-01 0.0163302923  0.760192898
## lapse_zoffset[49]      -6.482915e-01 0.0163230687  0.739144824
## lapse_zoffset[50]       1.495457e+00 0.0098652303  0.253515904
## lapse_zoffset[51]      -2.541884e-01 0.0193797660  0.799392847
## lapse_zoffset[52]      -1.522052e-01 0.0201321829  0.824457651
## lapse_zoffset[53]      -5.826488e-01 0.0151353332  0.724722297
## lapse_zoffset[54]      -4.903084e-01 0.0156009281  0.725875640
## lapse_zoffset[55]      -5.223139e-01 0.0169769682  0.774727159
## lapse_zoffset[56]      -6.519940e-01 0.0147550112  0.689545277
## lapse_zoffset[57]      -7.387347e-01 0.0163688555  0.735708122
## lapse_zoffset[58]      -6.251404e-01 0.0161470059  0.739427058
## lapse_zoffset[59]      -3.548243e-01 0.0180538301  0.779379656
## lapse_zoffset[60]       2.451630e-01 0.0193100119  0.662707081
## lapse_zoffset[61]      -4.651278e-01 0.0168457953  0.750648292
## lapse_zoffset[62]      -8.347546e-02 0.0173328264  0.658319901
## lapse_zoffset[63]      -1.360146e-01 0.0179685402  0.731731591
## lapse_zoffset[64]       5.219041e-02 0.0235682329  0.731230238
## lapse_zoffset[65]      -4.995131e-01 0.0162205002  0.759190412
## lapse_zoffset[66]      -2.013050e-01 0.0190495574  0.779127291
## lapse_zoffset[67]      -6.777250e-01 0.0137503740  0.744266735
## lapse_zoffset[68]       6.921330e-01 0.0217463155  0.565730459
## lapse_zoffset[69]      -6.483396e-01 0.0138721527  0.690494026
## lapse_zoffset[70]      -4.318392e-01 0.0168429275  0.736802317
## lapse_zoffset[71]       7.237670e-02 0.0226083899  0.767470644
## lapse_zoffset[72]       1.716941e+00 0.0101762987  0.265045764
## lapse_zoffset[73]      -7.785769e-02 0.0185463814  0.707320426
## lapse_zoffset[74]      -5.272899e-01 0.0154771184  0.728196031
## lapse_zoffset[75]      -4.814782e-01 0.0153642274  0.769052517
## lapse_zoffset[76]       2.272641e-01 0.0219226641  0.722058066
## lapse_zoffset[77]      -7.025220e-01 0.0125173757  0.700921255
## lapse_zoffset[78]      -5.353327e-01 0.0147507335  0.740883684
## lapse_zoffset[79]      -4.309058e-01 0.0164799428  0.756978123
## lapse_zoffset[80]       2.126794e-01 0.0194927167  0.650925798
## lapse_zoffset[81]      -1.591972e-01 0.0171339293  0.688130706
## lapse_zoffset[82]      -2.430407e-01 0.0186680990  0.816124354
## lapse_zoffset[83]      -5.725442e-01 0.0162209269  0.728286055
## lapse_zoffset[84]      -6.235124e-01 0.0140480821  0.725195160
## lapse_zoffset[85]      -6.474246e-01 0.0149641417  0.735382764
## lapse_zoffset[86]       9.042442e-01 0.0200116458  0.398201664
## lapse_zoffset[87]       1.021280e+00 0.0275511384  0.525891632
## lapse_zoffset[88]      -3.219270e-01 0.0171537214  0.776618668
## lapse_zoffset[89]       4.378443e-01 0.0196523724  0.646356958
## lapse_zoffset[90]       6.816194e-02 0.0230635022  0.836722686
## lapse_zoffset[91]      -6.084818e-01 0.0170259536  0.769821814
## lapse_zoffset[92]      -3.571542e-01 0.0166063899  0.763719835
## lapse_zoffset[93]       6.851632e-01 0.0289196463  0.638424384
## lapse_zoffset[94]       1.500216e+00 0.0097224081  0.247232013
## lapse_zoffset[95]      -4.514815e-01 0.0162932653  0.778113960
## lapse_zoffset[96]       1.143517e+00 0.0199167636  0.419595058
## lapse_zoffset[97]       1.932795e+00 0.0124309176  0.256451260
## lapse_zoffset[98]      -7.474136e-01 0.0160890016  0.732469091
## lapse_zoffset[99]      -1.769049e-01 0.0200828023  0.832433159
## lapse_zoffset[100]     -4.108219e-01 0.0178340828  0.803403655
## lapse_zoffset[101]      2.751720e-01 0.0233106950  0.722556952
## lapse_zoffset[102]     -6.095027e-01 0.0159439676  0.762057549
## lapse_zoffset[103]      1.660090e+00 0.0119290132  0.255117257
## lapse_zoffset[104]     -5.105916e-01 0.0177844264  0.763696816
## lapse_zoffset[105]     -3.570526e-01 0.0179522832  0.741043704
## lapse_zoffset[106]      5.295277e-02 0.0207807200  0.708516517
## lapse_zoffset[107]     -1.932501e-01 0.0225954157  0.844933095
## lapse_zoffset[108]     -5.290146e-01 0.0158157270  0.703815281
## lapse_zoffset[109]     -5.061068e-01 0.0151052528  0.772199630
## lapse_zoffset[110]      1.109593e+00 0.0204966659  0.407124579
## lapse_zoffset[111]     -5.411049e-01 0.0154557612  0.797589096
## lapse_zoffset[112]     -5.792436e-01 0.0165632764  0.737332742
## lapse_zoffset[113]     -6.430436e-01 0.0159721549  0.717233990
## lapse_zoffset[114]      1.080951e+00 0.0206578768  0.464002407
## lapse_zoffset[115]     -5.483109e-01 0.0147848718  0.746864301
## lapse_zoffset[116]     -4.943276e-01 0.0171857077  0.773338910
## lapse_zoffset[117]      2.083384e-01 0.0191422035  0.670676618
## lapse_zoffset[118]      1.434893e+00 0.0113520757  0.302906896
## lapse_zoffset[119]     -5.928068e-01 0.0158272261  0.715598359
## lapse_zoffset[120]     -4.396959e-01 0.0158316775  0.753929494
## lapse_zoffset[121]     -6.460430e-01 0.0156653659  0.713985078
## lapse_zoffset[122]     -5.634993e-01 0.0183820032  0.746118923
## lapse_zoffset[123]     -5.176762e-01 0.0176924012  0.766208232
## lapse_zoffset[124]     -4.131633e-01 0.0163126948  0.776762198
## lapse_zoffset[125]     -5.133291e-01 0.0170922233  0.785881049
## lapse_zoffset[126]      4.691765e-01 0.0255801660  0.699303808
## lapse_zoffset[127]      9.256093e-02 0.0202365762  0.814070160
## lapse_zoffset[128]      1.472334e+00 0.0121678539  0.301248885
## lapse_zoffset[129]     -6.291906e-01 0.0168409955  0.725039686
## lapse_zoffset[130]     -9.464164e-02 0.0192068563  0.788990265
## lapse_zoffset[131]     -5.248175e-01 0.0148570493  0.719321404
## lapse_zoffset[132]      6.661420e-01 0.0199122893  0.548671389
## lapse_zoffset[133]     -6.248505e-01 0.0154060825  0.752003077
## lapse_zoffset[134]     -3.996598e-01 0.0185550834  0.805540752
## lapse_zoffset[135]      1.856299e+00 0.0107183412  0.245215860
## lapse_zoffset[136]     -3.002751e-01 0.0176748782  0.801018420
## lapse_zoffset[137]     -5.064425e-01 0.0150882949  0.734397574
## lapse_zoffset[138]     -4.676429e-01 0.0154577554  0.748368126
## lapse_zoffset[139]     -3.393408e-01 0.0185182170  0.803829585
## lapse_zoffset[140]     -6.021896e-01 0.0163534584  0.771734992
## lapse_zoffset[141]     -2.430297e-01 0.0188197671  0.781236251
## lapse_zoffset[142]      5.640368e-01 0.0198235471  0.585266408
## lapse_zoffset[143]     -5.609870e-01 0.0169889484  0.766879082
## lapse_zoffset[144]     -1.502922e-01 0.0188104271  0.755852467
## lapse_zoffset[145]      6.639891e-01 0.0212462228  0.539671012
## lapse_zoffset[146]      4.257643e-01 0.0225117788  0.676705045
## lapse_zoffset[147]     -7.792449e-01 0.0145451608  0.699737993
## lapse_zoffset[148]      5.802248e-01 0.0215117035  0.610408835
## lapse_zoffset[149]     -5.774494e-01 0.0145944676  0.722189918
## lapse_zoffset[150]     -5.658090e-01 0.0152794601  0.749502462
## threshold[1]            2.620343e+00 0.0069441513  0.351480326
## threshold[2]            2.444291e+00 0.0058200660  0.300583279
## threshold[3]            2.362572e+00 0.0041081180  0.270588307
## threshold[4]            2.384648e+00 0.0055492060  0.290419005
## threshold[5]            2.370070e+00 0.0054673643  0.305761204
## threshold[6]            2.277109e+00 0.0055361826  0.239129926
## threshold[7]            2.472335e+00 0.0063281210  0.314049388
## threshold[8]            2.323102e+00 0.0051265155  0.290502410
## threshold[9]            2.428907e+00 0.0065061130  0.251032895
## threshold[10]           2.396663e+00 0.0055733419  0.301160468
## threshold[11]           2.397133e+00 0.0048681004  0.265301994
## threshold[12]           2.376203e+00 0.0049475996  0.274267398
## threshold[13]           2.548445e+00 0.0048996127  0.285010118
## threshold[14]           2.347145e+00 0.0058546380  0.317251737
## threshold[15]           2.513893e+00 0.0073491675  0.323574083
## threshold[16]           2.284926e+00 0.0046851806  0.264184841
## threshold[17]           2.335827e+00 0.0046511378  0.248120657
## threshold[18]           2.405588e+00 0.0069627238  0.271391838
## threshold[19]           2.585808e+00 0.0062982349  0.337209903
## threshold[20]           2.564256e+00 0.0050375875  0.284284278
## threshold[21]           2.418567e+00 0.0066903353  0.309205131
## threshold[22]           2.303722e+00 0.0046387613  0.266691397
## threshold[23]           2.494869e+00 0.0081102745  0.309371773
## threshold[24]           2.576463e+00 0.0063775590  0.327837146
## threshold[25]           2.739882e+00 0.0128926788  0.393990096
## threshold[26]           2.429279e+00 0.0073549648  0.332832549
## threshold[27]           2.619852e+00 0.0057702066  0.302575478
## threshold[28]           2.666285e+00 0.0079461089  0.339738636
## threshold[29]           2.779981e+00 0.0130447258  0.372709046
## threshold[30]           2.462460e+00 0.0094611524  0.352107172
## threshold[31]           2.333861e+00 0.0045677951  0.258242028
## threshold[32]           2.634827e+00 0.0079843678  0.359737383
## threshold[33]           2.457111e+00 0.0065613388  0.296485065
## threshold[34]           2.548867e+00 0.0051173546  0.282666492
## threshold[35]           2.611400e+00 0.0061581334  0.301706996
## threshold[36]           2.276085e+00 0.0060159734  0.262611696
## threshold[37]           2.430884e+00 0.0069255613  0.334143099
## threshold[38]           2.454123e+00 0.0064574568  0.294570704
## threshold[39]           2.238968e+00 0.0054362234  0.273596782
## threshold[40]           2.403508e+00 0.0075293808  0.264398204
## threshold[41]           2.571189e+00 0.0057993553  0.290193575
## threshold[42]           2.421667e+00 0.0073450956  0.344324332
## threshold[43]           2.458830e+00 0.0062665283  0.302673846
## threshold[44]           2.313236e+00 0.0046656149  0.253628455
## threshold[45]           2.333213e+00 0.0051405190  0.289966442
## threshold[46]           2.567539e+00 0.0063741503  0.327624584
## threshold[47]           2.192984e+00 0.0057627828  0.262592987
## threshold[48]           2.393289e+00 0.0069796436  0.268849757
## threshold[49]           2.388081e+00 0.0068598629  0.261658675
## threshold[50]           2.429219e+00 0.0089438270  0.381947904
## threshold[51]           2.373633e+00 0.0063196051  0.311900090
## threshold[52]           2.482486e+00 0.0075041246  0.338237007
## threshold[53]           2.230567e+00 0.0057450403  0.260537867
## threshold[54]           2.444607e+00 0.0068740647  0.302616436
## threshold[55]           2.680300e+00 0.0081377906  0.317537155
## threshold[56]           2.457815e+00 0.0065022157  0.267165908
## threshold[57]           2.226239e+00 0.0051155427  0.263687528
## threshold[58]           2.435587e+00 0.0064341227  0.293278284
## threshold[59]           2.547383e+00 0.0133522459  0.381449495
## threshold[60]           2.482813e+00 0.0097651471  0.331341018
## threshold[61]           2.495039e+00 0.0088089715  0.356856896
## threshold[62]           2.345134e+00 0.0050210385  0.288690566
## threshold[63]           2.435469e+00 0.0074530929  0.336882081
## threshold[64]           2.484185e+00 0.0106603006  0.348951813
## threshold[65]           2.492686e+00 0.0049483761  0.283565643
## threshold[66]           2.540352e+00 0.0122428757  0.382797957
## threshold[67]           2.430495e+00 0.0063072007  0.265702446
## threshold[68]           2.666211e+00 0.0080619014  0.341393926
## threshold[69]           2.269392e+00 0.0062570535  0.238318629
## threshold[70]           2.392918e+00 0.0074726242  0.268649197
## threshold[71]           2.582944e+00 0.0059070323  0.298816822
## threshold[72]           2.480655e+00 0.0094085162  0.354488208
## threshold[73]           2.398607e+00 0.0061667837  0.304975326
## threshold[74]           2.533717e+00 0.0048633178  0.276624842
## threshold[75]           2.626489e+00 0.0071571460  0.303919953
## threshold[76]           2.375654e+00 0.0054949871  0.281949780
## threshold[77]           2.157242e+00 0.0088341891  0.239974517
## threshold[78]           2.425039e+00 0.0047096099  0.283120406
## threshold[79]           2.403806e+00 0.0074059116  0.275727481
## threshold[80]           2.455312e+00 0.0070997976  0.329534370
## threshold[81]           2.277788e+00 0.0048925015  0.288400283
## threshold[82]           2.673033e+00 0.0080152365  0.346082947
## threshold[83]           2.641450e+00 0.0060249929  0.290649401
## threshold[84]           2.522982e+00 0.0049748000  0.263208077
## threshold[85]           2.267263e+00 0.0055832524  0.236001958
## threshold[86]           2.383599e+00 0.0059970595  0.302620236
## threshold[87]           2.443200e+00 0.0061175848  0.314633678
## threshold[88]           2.632070e+00 0.0066348883  0.298462624
## threshold[89]           2.657540e+00 0.0079597384  0.337551365
## threshold[90]           2.566535e+00 0.0110132162  0.367823715
## threshold[91]           2.247822e+00 0.0065975010  0.252814648
## threshold[92]           2.463389e+00 0.0081654393  0.335550988
## threshold[93]           2.406514e+00 0.0050067658  0.298383012
## threshold[94]           2.388259e+00 0.0069108976  0.323625822
## threshold[95]           2.416205e+00 0.0060349239  0.295390963
## threshold[96]           2.351537e+00 0.0057274982  0.302863625
## threshold[97]           2.535140e+00 0.0061180656  0.318627780
## threshold[98]           2.208796e+00 0.0052940890  0.259063279
## threshold[99]           2.665317e+00 0.0075232261  0.336896681
## threshold[100]          2.431318e+00 0.0054997749  0.290690863
## threshold[101]          2.390770e+00 0.0066439564  0.328350707
## threshold[102]          2.498663e+00 0.0051084291  0.275326408
## threshold[103]          2.592193e+00 0.0067548374  0.339667284
## threshold[104]          2.293287e+00 0.0058342855  0.268190996
## threshold[105]          2.545561e+00 0.0049614597  0.273639342
## threshold[106]          2.432842e+00 0.0066073313  0.316711381
## threshold[107]          3.053578e+00 0.0322613147  0.610298625
## threshold[108]          2.324027e+00 0.0049767101  0.282070726
## threshold[109]          2.371419e+00 0.0047230372  0.272189876
## threshold[110]          2.442365e+00 0.0086862050  0.352499243
## threshold[111]          2.425735e+00 0.0054780268  0.287448263
## threshold[112]          2.394966e+00 0.0065135809  0.295250514
## threshold[113]          2.274032e+00 0.0049579383  0.269820492
## threshold[114]          2.373717e+00 0.0051384014  0.288263786
## threshold[115]          2.312565e+00 0.0048060367  0.252971286
## threshold[116]          2.403473e+00 0.0045668362  0.267280827
## threshold[117]          2.661203e+00 0.0076162677  0.324829778
## threshold[118]          2.423661e+00 0.0060141138  0.316250093
## threshold[119]          2.480785e+00 0.0087012682  0.328692935
## threshold[120]          2.384167e+00 0.0046518348  0.265268079
## threshold[121]          2.387470e+00 0.0059649972  0.288853294
## threshold[122]          2.368571e+00 0.0038192179  0.243400132
## threshold[123]          2.383549e+00 0.0046889830  0.278415478
## threshold[124]          2.499698e+00 0.0082201249  0.311733452
## threshold[125]          2.686776e+00 0.0079262887  0.328740256
## threshold[126]          2.471259e+00 0.0064362433  0.324092674
## threshold[127]          2.527737e+00 0.0106123839  0.332908064
## threshold[128]          2.370369e+00 0.0056589376  0.302786030
## threshold[129]          2.246829e+00 0.0065009285  0.247147860
## threshold[130]          2.672547e+00 0.0087357635  0.338560384
## threshold[131]          2.550734e+00 0.0051977636  0.271494438
## threshold[132]          2.442915e+00 0.0074340222  0.331236301
## threshold[133]          2.331355e+00 0.0050291549  0.288661139
## threshold[134]          2.492466e+00 0.0078982697  0.316199249
## threshold[135]          2.368875e+00 0.0058765779  0.328582037
## threshold[136]          2.498952e+00 0.0083558929  0.343491767
## threshold[137]          2.519869e+00 0.0047979281  0.261160291
## threshold[138]          2.647322e+00 0.0067465649  0.311086558
## threshold[139]          2.548952e+00 0.0095745242  0.343972714
## threshold[140]          2.349875e+00 0.0046828531  0.269250041
## threshold[141]          2.383722e+00 0.0061264925  0.297320959
## threshold[142]          2.636515e+00 0.0066941512  0.328271065
## threshold[143]          2.440615e+00 0.0049574150  0.272578317
## threshold[144]          2.424591e+00 0.0064887320  0.306596226
## threshold[145]          2.373934e+00 0.0062198267  0.296821242
## threshold[146]          2.479225e+00 0.0065394951  0.305386677
## threshold[147]          2.105106e+00 0.0095390935  0.258721953
## threshold[148]          2.600631e+00 0.0056966617  0.306560056
## threshold[149]          2.443392e+00 0.0058582323  0.271231212
## threshold[150]          2.349233e+00 0.0047147630  0.268295281
## spread[1]               1.824541e+00 0.0180566330  0.580297272
## spread[2]               1.853861e+00 0.0119301288  0.421861280
## spread[3]               1.708394e+00 0.0110248064  0.414239845
## spread[4]               2.181866e+00 0.0118587836  0.439498593
## spread[5]               2.106796e+00 0.0149573340  0.548211695
## spread[6]               1.348277e+00 0.0061980919  0.289811045
## spread[7]               1.875669e+00 0.0099589580  0.405102180
## spread[8]               2.151093e+00 0.0268668613  0.653341807
## spread[9]               1.274473e+00 0.0081089682  0.284783082
## spread[10]              2.027651e+00 0.0263110742  0.620158379
## spread[11]              1.632741e+00 0.0098429040  0.421687416
## spread[12]              1.664456e+00 0.0071804958  0.355854979
## spread[13]              1.411999e+00 0.0055247694  0.300786253
## spread[14]              1.880700e+00 0.0139223975  0.599071822
## spread[15]              1.952503e+00 0.0181050480  0.513747437
## spread[16]              1.521628e+00 0.0065456212  0.327377110
## spread[17]              1.681603e+00 0.0079806580  0.388712845
## spread[18]              1.386060e+00 0.0059122975  0.297677714
## spread[19]              1.633403e+00 0.0112008433  0.500233130
## spread[20]              1.593042e+00 0.0059037876  0.317847695
## spread[21]              2.077178e+00 0.0096685672  0.409620458
## spread[22]              1.731364e+00 0.0061516133  0.347658743
## spread[23]              1.763085e+00 0.0092389435  0.381944863
## spread[24]              1.636383e+00 0.0094079634  0.482965469
## spread[25]              1.948483e+00 0.0160310158  0.499597699
## spread[26]              2.036982e+00 0.0167486735  0.579477352
## spread[27]              1.505466e+00 0.0060937611  0.299106464
## spread[28]              1.849715e+00 0.0096247146  0.404197416
## spread[29]              1.683968e+00 0.0082104128  0.343006145
## spread[30]              2.094959e+00 0.0333928516  0.677992738
## spread[31]              1.439725e+00 0.0061664196  0.311977478
## spread[32]              1.792039e+00 0.0233516451  0.617443050
## spread[33]              1.760472e+00 0.0070418050  0.341430357
## spread[34]              1.627920e+00 0.0065275556  0.337606440
## spread[35]              1.561159e+00 0.0061149124  0.339206543
## spread[36]              1.595833e+00 0.0063262061  0.334023312
## spread[37]              1.890057e+00 0.0207041211  0.608660881
## spread[38]              1.735940e+00 0.0080651898  0.365663616
## spread[39]              1.928837e+00 0.0091437845  0.436884038
## spread[40]              1.320136e+00 0.0071409396  0.281724631
## spread[41]              1.578659e+00 0.0085393363  0.400323106
## spread[42]              2.017089e+00 0.0171922049  0.602630646
## spread[43]              1.858384e+00 0.0197319008  0.561549398
## spread[44]              1.586410e+00 0.0056470348  0.318999740
## spread[45]              1.677945e+00 0.0066278435  0.354312769
## spread[46]              1.607583e+00 0.0093916129  0.459895626
## spread[47]              1.369913e+00 0.0082234777  0.325149496
## spread[48]              1.463813e+00 0.0062649258  0.327342432
## spread[49]              1.361874e+00 0.0053457655  0.285402447
## spread[50]              2.133386e+00 0.0179670395  0.642264201
## spread[51]              2.149122e+00 0.0147574482  0.485900577
## spread[52]              1.976580e+00 0.0113839454  0.425973993
## spread[53]              1.540234e+00 0.0070152754  0.350314478
## spread[54]              1.766636e+00 0.0078658507  0.373516636
## spread[55]              1.592808e+00 0.0065630123  0.320085118
## spread[56]              1.291474e+00 0.0065639860  0.299394802
## spread[57]              1.565336e+00 0.0065454512  0.338287015
## spread[58]              1.563575e+00 0.0070464485  0.334460775
## spread[59]              2.130860e+00 0.0124209702  0.439408825
## spread[60]              2.093758e+00 0.0143944356  0.546863096
## spread[61]              2.003407e+00 0.0085601970  0.397575983
## spread[62]              1.679319e+00 0.0092419961  0.432332249
## spread[63]              2.148451e+00 0.0135781451  0.489428128
## spread[64]              2.225328e+00 0.0188517711  0.526697354
## spread[65]              1.858006e+00 0.0078561824  0.371131383
## spread[66]              2.033383e+00 0.0103100204  0.439926795
## spread[67]              1.343799e+00 0.0062659584  0.286087027
## spread[68]              1.666697e+00 0.0145277866  0.489247164
## spread[69]              1.151362e+00 0.0076265386  0.269947373
## spread[70]              1.599324e+00 0.0070636262  0.362223184
## spread[71]              1.845012e+00 0.0105289672  0.445591267
## spread[72]              1.844535e+00 0.0158306458  0.552510972
## spread[73]              1.907062e+00 0.0115821955  0.469335561
## spread[74]              1.594904e+00 0.0068526715  0.342548445
## spread[75]              1.705479e+00 0.0067900264  0.330833506
## spread[76]              1.672892e+00 0.0116598088  0.435531457
## spread[77]              1.058922e+00 0.0099957516  0.268287463
## spread[78]              1.493882e+00 0.0056334643  0.300838129
## spread[79]              1.690474e+00 0.0072630096  0.361321524
## spread[80]              2.008202e+00 0.0134772162  0.529891005
## spread[81]              1.935477e+00 0.0105584614  0.472489676
## spread[82]              1.804968e+00 0.0084019994  0.387843890
## spread[83]              1.520904e+00 0.0062475527  0.320968304
## spread[84]              1.253651e+00 0.0067632199  0.286783947
## spread[85]              1.256246e+00 0.0069754331  0.289719328
## spread[86]              1.746418e+00 0.0205985753  0.535921565
## spread[87]              1.809061e+00 0.0293065780  0.629018566
## spread[88]              1.734528e+00 0.0073846120  0.358202442
## spread[89]              1.788940e+00 0.0128665554  0.486973458
## spread[90]              2.114895e+00 0.0176109042  0.491914479
## spread[91]              1.381125e+00 0.0053059354  0.299858681
## spread[92]              2.020352e+00 0.0089306989  0.418376083
## spread[93]              1.880749e+00 0.0266455217  0.576891994
## spread[94]              1.928459e+00 0.0163027841  0.599501312
## spread[95]              1.745093e+00 0.0073356315  0.349861549
## spread[96]              1.742731e+00 0.0266664858  0.626259606
## spread[97]              1.692775e+00 0.0106704160  0.505586152
## spread[98]              1.444080e+00 0.0082872905  0.338315757
## spread[99]              1.870413e+00 0.0101994083  0.397577742
## spread[100]             1.784097e+00 0.0079515179  0.357402943
## spread[101]             2.455294e+00 0.0246683359  0.665417075
## spread[102]             1.467535e+00 0.0059919234  0.313501444
## spread[103]             1.694708e+00 0.0119229078  0.525844844
## spread[104]             1.765734e+00 0.0077632496  0.388312500
## spread[105]             1.598467e+00 0.0067205751  0.343757401
## spread[106]             2.142136e+00 0.0153692176  0.516116743
## spread[107]             1.966713e+00 0.0189748348  0.472957470
## spread[108]             1.884706e+00 0.0072207597  0.386404568
## spread[109]             1.625674e+00 0.0062613457  0.330860756
## spread[110]             2.172059e+00 0.0315017645  0.725774867
## spread[111]             1.533595e+00 0.0064562203  0.313344500
## spread[112]             1.745851e+00 0.0065681744  0.360051139
## spread[113]             1.660022e+00 0.0068091078  0.363692433
## spread[114]             1.844697e+00 0.0241494851  0.609579792
## spread[115]             1.615637e+00 0.0066463136  0.332460057
## spread[116]             1.534408e+00 0.0064408432  0.331631833
## spread[117]             1.730302e+00 0.0104057651  0.427093743
## spread[118]             1.788706e+00 0.0175848026  0.568829362
## spread[119]             1.704217e+00 0.0065539011  0.346679829
## spread[120]             1.934746e+00 0.0107363540  0.385651762
## spread[121]             1.714334e+00 0.0064877298  0.338257240
## spread[122]             1.335885e+00 0.0047339848  0.274731084
## spread[123]             1.529570e+00 0.0063656366  0.317145052
## spread[124]             1.784522e+00 0.0077024225  0.358005599
## spread[125]             1.593680e+00 0.0062740952  0.314069731
## spread[126]             1.790170e+00 0.0152462600  0.493297473
## spread[127]             1.947118e+00 0.0139623617  0.462353279
## spread[128]             1.583195e+00 0.0191623504  0.514400343
## spread[129]             1.366903e+00 0.0063738546  0.298388386
## spread[130]             1.852028e+00 0.0107809027  0.388491712
## spread[131]             1.362949e+00 0.0059572875  0.294883178
## spread[132]             2.097872e+00 0.0232393936  0.652274578
## spread[133]             1.674246e+00 0.0063838695  0.360253376
## spread[134]             1.768296e+00 0.0077049290  0.347595610
## spread[135]             1.855434e+00 0.0116236919  0.533795387
## spread[136]             2.025335e+00 0.0129182411  0.412878971
## spread[137]             1.434830e+00 0.0054125736  0.303660114
## spread[138]             1.528902e+00 0.0062359723  0.310389872
## spread[139]             1.784671e+00 0.0108790028  0.350724260
## spread[140]             1.407377e+00 0.0050749013  0.299062746
## spread[141]             2.105257e+00 0.0111957758  0.492723838
## spread[142]             1.542549e+00 0.0123290737  0.464112688
## spread[143]             1.486324e+00 0.0060716396  0.314390475
## spread[144]             1.940411e+00 0.0089511317  0.429328177
## spread[145]             2.043201e+00 0.0243591941  0.629578809
## spread[146]             1.731750e+00 0.0156314271  0.480827234
## spread[147]             1.291197e+00 0.0096114578  0.331343652
## spread[148]             1.746217e+00 0.0144039183  0.509444537
## spread[149]             1.418546e+00 0.0053674896  0.273591786
## spread[150]             1.460797e+00 0.0062780616  0.302220014
## lapse[1]                1.036191e-01 0.0011176423  0.040866097
## lapse[2]                1.740382e-02 0.0004769875  0.020177750
## lapse[3]                1.897936e-02 0.0003682902  0.018082018
## lapse[4]                1.386077e-02 0.0004162981  0.016794272
## lapse[5]                2.924525e-02 0.0006512165  0.025853881
## lapse[6]                6.475365e-03 0.0001918962  0.008813984
## lapse[7]                1.445809e-02 0.0003999735  0.017630948
## lapse[8]                4.658705e-02 0.0011169528  0.032591807
## lapse[9]                6.164913e-03 0.0001647733  0.007999902
## lapse[10]               4.804814e-02 0.0012482516  0.034319083
## lapse[11]               2.293325e-02 0.0004302561  0.020411655
## lapse[12]               8.809973e-03 0.0002173159  0.010745542
## lapse[13]               6.321151e-03 0.0001554539  0.008013144
## lapse[14]               1.754998e-01 0.0008847828  0.042063514
## lapse[15]               3.162915e-02 0.0009188842  0.030596757
## lapse[16]               7.148945e-03 0.0001741962  0.009202111
## lapse[17]               1.144275e-02 0.0002954621  0.013292900
## lapse[18]               6.627415e-03 0.0001744247  0.008371803
## lapse[19]               3.055945e-01 0.0008889376  0.042942279
## lapse[20]               8.371378e-03 0.0002613983  0.011426465
## lapse[21]               1.388446e-02 0.0003888759  0.017208503
## lapse[22]               7.519963e-03 0.0002068384  0.009602896
## lapse[23]               1.373136e-02 0.0003625989  0.016923914
## lapse[24]               3.789663e-01 0.0010057960  0.046255875
## lapse[25]               3.470031e-02 0.0007521844  0.030445742
## lapse[26]               4.321070e-02 0.0009021553  0.032605723
## lapse[27]               7.307764e-03 0.0001914448  0.009715021
## lapse[28]               1.769405e-02 0.0004841276  0.020153971
## lapse[29]               1.012011e-02 0.0003278112  0.014180895
## lapse[30]               9.235608e-02 0.0016664577  0.042297674
## lapse[31]               6.529406e-03 0.0001860562  0.008492468
## lapse[32]               1.037651e-01 0.0011177165  0.041229721
## lapse[33]               9.581101e-03 0.0002426445  0.012373254
## lapse[34]               1.070218e-02 0.0002565016  0.013041554
## lapse[35]               1.036222e-02 0.0002689875  0.012957962
## lapse[36]               7.504837e-03 0.0002062819  0.010247430
## lapse[37]               1.227706e-01 0.0011202013  0.043982364
## lapse[38]               9.794841e-03 0.0002454580  0.013364867
## lapse[39]               1.000240e-02 0.0002506846  0.011540652
## lapse[40]               5.639213e-03 0.0001349139  0.007005527
## lapse[41]               1.834837e-02 0.0004398243  0.018559752
## lapse[42]               2.065042e-01 0.0008609341  0.045929588
## lapse[43]               4.367270e-02 0.0008552371  0.032603603
## lapse[44]               7.865406e-03 0.0002249900  0.010954993
## lapse[45]               8.853747e-03 0.0002485478  0.011014157
## lapse[46]               3.609870e-01 0.0010813155  0.046227752
## lapse[47]               6.120091e-03 0.0001712874  0.007552938
## lapse[48]               7.082311e-03 0.0001927965  0.009459169
## lapse[49]               6.308862e-03 0.0002125960  0.008739449
## lapse[50]               2.017000e-01 0.0009234542  0.044863704
## lapse[51]               1.849332e-02 0.0005160492  0.021260547
## lapse[52]               1.551677e-02 0.0004357424  0.018597621
## lapse[53]               9.131947e-03 0.0002198237  0.011197217
## lapse[54]               1.109254e-02 0.0002885988  0.013514307
## lapse[55]               8.526205e-03 0.0002600209  0.011378778
## lapse[56]               5.750471e-03 0.0001495789  0.007353544
## lapse[57]               6.981577e-03 0.0001966539  0.009605325
## lapse[58]               8.740074e-03 0.0002528465  0.011218734
## lapse[59]               1.530800e-02 0.0004249029  0.018641142
## lapse[60]               3.534432e-02 0.0007472414  0.029477162
## lapse[61]               1.196786e-02 0.0003109995  0.015069620
## lapse[62]               1.964342e-02 0.0003744254  0.018253669
## lapse[63]               2.112580e-02 0.0005782310  0.022990473
## lapse[64]               2.810803e-02 0.0006798942  0.027219206
## lapse[65]               8.780729e-03 0.0002578739  0.011703278
## lapse[66]               1.969246e-02 0.0005265232  0.021924918
## lapse[67]               6.238877e-03 0.0001975248  0.008690480
## lapse[68]               5.049241e-02 0.0008748256  0.030328247
## lapse[69]               5.039659e-03 0.0001369375  0.006435998
## lapse[70]               9.359403e-03 0.0002343939  0.011473667
## lapse[71]               2.341653e-02 0.0005840420  0.023677875
## lapse[72]               1.984329e-01 0.0009317573  0.043500750
## lapse[73]               2.105327e-02 0.0004462982  0.020031496
## lapse[74]               7.742780e-03 0.0002178529  0.010266772
## lapse[75]               9.378440e-03 0.0002773536  0.013076990
## lapse[76]               2.386760e-02 0.0005140960  0.021477277
## lapse[77]               4.629438e-03 0.0001257736  0.006176479
## lapse[78]               6.757980e-03 0.0001895854  0.009023840
## lapse[79]               9.681566e-03 0.0002385657  0.012059080
## lapse[80]               3.275190e-02 0.0006280892  0.026799233
## lapse[81]               1.781770e-02 0.0003295492  0.017650472
## lapse[82]               1.458904e-02 0.0003908843  0.017586692
## lapse[83]               7.295156e-03 0.0002244153  0.009885037
## lapse[84]               6.444312e-03 0.0001627893  0.008210979
## lapse[85]               5.283590e-03 0.0001316903  0.006770891
## lapse[86]               8.356872e-02 0.0010332820  0.037913854
## lapse[87]               7.440426e-02 0.0013845566  0.038518571
## lapse[88]               1.231216e-02 0.0003439860  0.015431894
## lapse[89]               3.639981e-02 0.0006884703  0.028336768
## lapse[90]               2.328758e-02 0.0007346851  0.026002497
## lapse[91]               6.099569e-03 0.0001672222  0.008139306
## lapse[92]               1.472981e-02 0.0003886254  0.017001139
## lapse[93]               4.739123e-02 0.0009024975  0.032080249
## lapse[94]               2.027777e-01 0.0009380324  0.043785555
## lapse[95]               8.542762e-03 0.0002624306  0.011792612
## lapse[96]               8.506611e-02 0.0012731594  0.036081096
## lapse[97]               3.030348e-01 0.0009698645  0.046913236
## lapse[98]               6.784295e-03 0.0002017056  0.008982260
## lapse[99]               1.713316e-02 0.0004715324  0.020535914
## lapse[100]              9.299226e-03 0.0002386217  0.012306160
## lapse[101]              4.041922e-02 0.0010224394  0.034738623
## lapse[102]              7.111443e-03 0.0002027573  0.009904794
## lapse[103]              2.050665e-01 0.0008281701  0.040848956
## lapse[104]              1.104605e-02 0.0002566533  0.013445681
## lapse[105]              1.097801e-02 0.0002879890  0.013473719
## lapse[106]              2.738182e-02 0.0006353847  0.025709937
## lapse[107]              1.811439e-02 0.0005479753  0.023767281
## lapse[108]              9.824564e-03 0.0002481667  0.011871096
## lapse[109]              7.669447e-03 0.0002311331  0.010579096
## lapse[110]              1.177573e-01 0.0016633855  0.047526821
## lapse[111]              7.338701e-03 0.0002250038  0.010526665
## lapse[112]              9.408502e-03 0.0002454261  0.012002690
## lapse[113]              8.186379e-03 0.0002121183  0.010544514
## lapse[114]              7.947978e-02 0.0011989795  0.038725066
## lapse[115]              6.690230e-03 0.0001899519  0.008966253
## lapse[116]              7.627162e-03 0.0002383904  0.010763663
## lapse[117]              2.561959e-02 0.0004583829  0.023668928
## lapse[118]              1.295085e-01 0.0009947477  0.040151958
## lapse[119]              8.902239e-03 0.0002235097  0.011139361
## lapse[120]              8.535332e-03 0.0002485098  0.011615307
## lapse[121]              8.019031e-03 0.0002079438  0.010019130
## lapse[122]              6.444005e-03 0.0001883400  0.008531862
## lapse[123]              7.428270e-03 0.0002205401  0.010025461
## lapse[124]              8.955033e-03 0.0002606266  0.012111220
## lapse[125]              9.047081e-03 0.0002907492  0.012345764
## lapse[126]              3.499723e-02 0.0007117714  0.027985788
## lapse[127]              2.232456e-02 0.0005452520  0.023506166
## lapse[128]              1.366621e-01 0.0009786660  0.039035886
## lapse[129]              5.454611e-03 0.0001768542  0.007302139
## lapse[130]              1.832076e-02 0.0004447802  0.020991750
## lapse[131]              7.678065e-03 0.0001866727  0.009531340
## lapse[132]              6.322287e-02 0.0011074637  0.037139347
## lapse[133]              8.719855e-03 0.0002477582  0.011065518
## lapse[134]              1.007308e-02 0.0003390546  0.014246024
## lapse[135]              3.333293e-01 0.0009421343  0.044789263
## lapse[136]              1.181609e-02 0.0003592481  0.016156637
## lapse[137]              8.037018e-03 0.0001877219  0.010005456
## lapse[138]              9.070338e-03 0.0002601781  0.012062967
## lapse[139]              1.097218e-02 0.0003524057  0.014722776
## lapse[140]              6.357707e-03 0.0001900456  0.008853039
## lapse[141]              1.855167e-02 0.0004939012  0.021400195
## lapse[142]              4.130045e-02 0.0006662657  0.027758051
## lapse[143]              6.826410e-03 0.0001925439  0.009337732
## lapse[144]              2.010988e-02 0.0004258362  0.021324879
## lapse[145]              6.142936e-02 0.0010315042  0.035149798
## lapse[146]              3.150939e-02 0.0006206761  0.025397274
## lapse[147]              5.978181e-03 0.0001501429  0.007551552
## lapse[148]              4.380102e-02 0.0006795669  0.030709752
## lapse[149]              7.192731e-03 0.0001893868  0.009494871
## lapse[150]              6.497641e-03 0.0001886289  0.008575138
## lp__                   -6.486936e+03 0.7747091211 18.379509918
##                                 2.5%           25%           50%
## sigma_log_threshold     9.345159e-03  6.997544e-02  1.124728e-01
## sigma_log_spread        1.449195e-01  2.199796e-01  2.599721e-01
## sigma_logit_lapse       1.542124e+00  1.807051e+00  1.958691e+00
## b_threshold[1]          8.296452e-01  9.046432e-01  9.404361e-01
## b_threshold[2]          7.572449e-01  8.323873e-01  8.705259e-01
## b_threshold[3]          7.265100e-01  8.143417e-01  8.587384e-01
## b_spread[1]             2.853101e-01  3.905803e-01  4.440814e-01
## b_spread[2]             3.058491e-01  4.205023e-01  4.729769e-01
## b_spread[3]             4.214857e-01  5.384892e-01  5.987782e-01
## b_lapse[1]             -5.556520e+00 -4.924277e+00 -4.593624e+00
## b_lapse[2]             -5.753747e+00 -5.102776e+00 -4.760292e+00
## b_lapse[3]             -5.334279e+00 -4.639188e+00 -4.296776e+00
## threshold_zoffset[1]   -1.878880e+00 -5.075408e-01  1.193398e-01
## threshold_zoffset[2]   -1.708489e+00 -5.182429e-01  1.645747e-01
## threshold_zoffset[3]   -1.916782e+00 -6.934494e-01 -9.572805e-02
## threshold_zoffset[4]   -1.726455e+00 -5.274195e-01  6.656716e-02
## threshold_zoffset[5]   -1.852355e+00 -6.814094e-01  1.940578e-03
## threshold_zoffset[6]   -2.062390e+00 -9.750322e-01 -3.902131e-01
## threshold_zoffset[7]   -1.702814e+00 -4.382420e-01  2.756759e-01
## threshold_zoffset[8]   -2.035694e+00 -7.778991e-01 -1.247072e-01
## threshold_zoffset[9]   -2.059711e+00 -9.905024e-01 -4.399414e-01
## threshold_zoffset[10]  -1.976618e+00 -6.449796e-01  3.027261e-03
## threshold_zoffset[11]  -1.845575e+00 -6.186047e-01  8.343348e-03
## threshold_zoffset[12]  -1.911539e+00 -5.682394e-01  3.366213e-02
## threshold_zoffset[13]  -1.924421e+00 -6.745216e-01 -6.334274e-02
## threshold_zoffset[14]  -2.057760e+00 -7.318096e-01 -8.401600e-02
## threshold_zoffset[15]  -1.609274e+00 -2.898319e-01  3.906173e-01
## threshold_zoffset[16]  -2.051082e+00 -8.548644e-01 -2.527533e-01
## threshold_zoffset[17]  -1.933066e+00 -8.063829e-01 -1.982142e-01
## threshold_zoffset[18]  -2.366925e+00 -1.183309e+00 -5.685132e-01
## threshold_zoffset[19]  -1.950763e+00 -6.693299e-01  9.557828e-03
## threshold_zoffset[20]  -1.878878e+00 -6.355707e-01 -1.923898e-02
## threshold_zoffset[21]  -1.772896e+00 -5.268882e-01  1.512694e-01
## threshold_zoffset[22]  -1.956660e+00 -8.337116e-01 -1.844299e-01
## threshold_zoffset[23]  -1.671281e+00 -3.269621e-01  3.247135e-01
## threshold_zoffset[24]  -1.971195e+00 -7.058765e-01 -1.574602e-02
## threshold_zoffset[25]  -1.646303e+00 -2.138007e-01  4.674952e-01
## threshold_zoffset[26]  -1.839026e+00 -5.163806e-01  1.905228e-01
## threshold_zoffset[27]  -1.763951e+00 -4.433642e-01  1.864171e-01
## threshold_zoffset[28]  -1.867459e+00 -3.686068e-01  2.740849e-01
## threshold_zoffset[29]  -1.471687e+00 -7.008750e-02  6.230516e-01
## threshold_zoffset[30]  -1.734297e+00 -4.537162e-01  2.520766e-01
## threshold_zoffset[31]  -2.008828e+00 -8.284830e-01 -2.186309e-01
## threshold_zoffset[32]  -1.886789e+00 -5.560266e-01  1.821282e-01
## threshold_zoffset[33]  -2.183740e+00 -9.878920e-01 -3.445130e-01
## threshold_zoffset[34]  -1.886210e+00 -6.563621e-01 -4.544149e-02
## threshold_zoffset[35]  -1.731795e+00 -4.804514e-01  1.384049e-01
## threshold_zoffset[36]  -2.266887e+00 -1.033383e+00 -3.905433e-01
## threshold_zoffset[37]  -1.860717e+00 -5.957015e-01  7.831360e-02
## threshold_zoffset[38]  -1.667246e+00 -4.479032e-01  1.947063e-01
## threshold_zoffset[39]  -2.263684e+00 -1.064661e+00 -4.433362e-01
## threshold_zoffset[40]  -2.207947e+00 -1.133350e+00 -5.438318e-01
## threshold_zoffset[41]  -1.802022e+00 -5.906091e-01  2.209821e-02
## threshold_zoffset[42]  -1.738927e+00 -5.200511e-01  1.513002e-01
## threshold_zoffset[43]  -1.745234e+00 -4.295765e-01  2.246457e-01
## threshold_zoffset[44]  -2.056851e+00 -8.662544e-01 -2.458666e-01
## threshold_zoffset[45]  -1.962131e+00 -7.373919e-01 -1.152092e-01
## threshold_zoffset[46]  -1.888426e+00 -6.806622e-01 -2.022123e-02
## threshold_zoffset[47]  -2.498163e+00 -1.229500e+00 -6.167522e-01
## threshold_zoffset[48]  -2.358254e+00 -1.154125e+00 -5.929280e-01
## threshold_zoffset[49]  -2.306810e+00 -1.189126e+00 -6.064364e-01
## threshold_zoffset[50]  -1.915379e+00 -5.688389e-01  1.444679e-01
## threshold_zoffset[51]  -2.032154e+00 -6.909076e-01  2.984455e-02
## threshold_zoffset[52]  -1.762496e+00 -4.110789e-01  2.901394e-01
## threshold_zoffset[53]  -2.130154e+00 -1.113475e+00 -4.821745e-01
## threshold_zoffset[54]  -1.636029e+00 -3.447828e-01  2.644040e-01
## threshold_zoffset[55]  -1.552147e+00 -3.011367e-01  3.278161e-01
## threshold_zoffset[56]  -2.050740e+00 -9.639186e-01 -3.398148e-01
## threshold_zoffset[57]  -2.257709e+00 -1.114644e+00 -4.896425e-01
## threshold_zoffset[58]  -1.523286e+00 -3.411899e-01  2.634506e-01
## threshold_zoffset[59]  -1.565768e+00 -1.700894e-01  5.444971e-01
## threshold_zoffset[60]  -1.587885e+00 -2.967436e-01  3.632840e-01
## threshold_zoffset[61]  -1.583667e+00 -2.858357e-01  3.711181e-01
## threshold_zoffset[62]  -1.955492e+00 -7.146021e-01 -4.199558e-02
## threshold_zoffset[63]  -1.803827e+00 -4.504142e-01  2.056653e-01
## threshold_zoffset[64]  -1.544310e+00 -2.670915e-01  3.391061e-01
## threshold_zoffset[65]  -2.033197e+00 -8.654735e-01 -2.526567e-01
## threshold_zoffset[66]  -1.480078e+00 -1.850036e-01  5.497972e-01
## threshold_zoffset[67]  -2.216791e+00 -1.031887e+00 -4.503107e-01
## threshold_zoffset[68]  -1.794525e+00 -3.994518e-01  2.767221e-01
## threshold_zoffset[69]  -2.211188e+00 -1.004092e+00 -4.114998e-01
## threshold_zoffset[70]  -2.306136e+00 -1.207444e+00 -5.731874e-01
## threshold_zoffset[71]  -1.820448e+00 -5.728207e-01  2.772788e-02
## threshold_zoffset[72]  -1.815657e+00 -4.507344e-01  2.019319e-01
## threshold_zoffset[73]  -1.721047e+00 -5.326936e-01  1.040154e-01
## threshold_zoffset[74]  -1.768837e+00 -6.789911e-01 -1.100326e-01
## threshold_zoffset[75]  -1.763004e+00 -4.484043e-01  2.266533e-01
## threshold_zoffset[76]  -2.016150e+00 -6.801283e-01 -6.871029e-02
## threshold_zoffset[77]  -2.582437e+00 -1.443212e+00 -9.054538e-01
## threshold_zoffset[78]  -1.739612e+00 -5.282352e-01  1.091340e-01
## threshold_zoffset[79]  -2.262142e+00 -1.161268e+00 -5.596833e-01
## threshold_zoffset[80]  -1.661616e+00 -3.884564e-01  2.953051e-01
## threshold_zoffset[81]  -2.165996e+00 -9.962732e-01 -3.149969e-01
## threshold_zoffset[82]  -1.569906e+00 -4.324985e-01  3.057706e-01
## threshold_zoffset[83]  -1.618982e+00 -3.831178e-01  2.395425e-01
## threshold_zoffset[84]  -1.813004e+00 -7.404016e-01 -1.610395e-01
## threshold_zoffset[85]  -2.133881e+00 -9.650944e-01 -4.211729e-01
## threshold_zoffset[86]  -1.802553e+00 -5.968744e-01  6.315612e-02
## threshold_zoffset[87]  -1.874355e+00 -5.383753e-01  1.463211e-01
## threshold_zoffset[88]  -1.536699e+00 -3.801724e-01  2.061196e-01
## threshold_zoffset[89]  -1.678687e+00 -4.316226e-01  2.459519e-01
## threshold_zoffset[90]  -1.593532e+00 -2.304349e-01  5.277836e-01
## threshold_zoffset[91]  -2.333794e+00 -1.096176e+00 -4.853527e-01
## threshold_zoffset[92]  -1.815840e+00 -4.082546e-01  3.284505e-01
## threshold_zoffset[93]  -1.921682e+00 -5.975776e-01  4.197965e-02
## threshold_zoffset[94]  -1.934139e+00 -6.276730e-01  7.801492e-02
## threshold_zoffset[95]  -1.844373e+00 -5.553345e-01  5.463584e-02
## threshold_zoffset[96]  -2.073165e+00 -8.456887e-01 -1.601701e-01
## threshold_zoffset[97]  -2.048098e+00 -7.871722e-01 -1.162461e-01
## threshold_zoffset[98]  -2.277701e+00 -1.182605e+00 -5.550153e-01
## threshold_zoffset[99]  -1.670114e+00 -3.645963e-01  2.745170e-01
## threshold_zoffset[100] -1.871386e+00 -5.038787e-01  1.233054e-01
## threshold_zoffset[101] -1.918928e+00 -6.093423e-01  8.398210e-02
## threshold_zoffset[102] -2.090134e+00 -8.111996e-01 -2.122709e-01
## threshold_zoffset[103] -1.875119e+00 -6.117731e-01  4.433453e-02
## threshold_zoffset[104] -2.110181e+00 -8.475776e-01 -2.794020e-01
## threshold_zoffset[105] -1.773802e+00 -6.357270e-01 -8.221817e-02
## threshold_zoffset[106] -1.737210e+00 -4.650662e-01  1.958012e-01
## threshold_zoffset[107] -1.163000e+00  3.479932e-01  1.165113e+00
## threshold_zoffset[108] -2.029189e+00 -8.809009e-01 -1.482114e-01
## threshold_zoffset[109] -1.876701e+00 -7.138234e-01 -4.531518e-02
## threshold_zoffset[110] -1.790718e+00 -4.087820e-01  2.052580e-01
## threshold_zoffset[111] -1.777483e+00 -5.288800e-01  1.332083e-01
## threshold_zoffset[112] -1.744092e+00 -5.431092e-01  6.281307e-02
## threshold_zoffset[113] -2.184777e+00 -9.407391e-01 -3.145631e-01
## threshold_zoffset[114] -1.950683e+00 -7.332463e-01 -7.916546e-02
## threshold_zoffset[115] -2.072062e+00 -9.049790e-01 -2.700706e-01
## threshold_zoffset[116] -1.675374e+00 -6.023859e-01  3.605190e-02
## threshold_zoffset[117] -1.589214e+00 -3.675170e-01  2.756592e-01
## threshold_zoffset[118] -1.854926e+00 -5.640078e-01  8.961580e-02
## threshold_zoffset[119] -1.552068e+00 -2.911466e-01  3.707920e-01
## threshold_zoffset[120] -1.945483e+00 -6.340317e-01  9.416666e-04
## threshold_zoffset[121] -1.756288e+00 -5.355873e-01  8.457756e-02
## threshold_zoffset[122] -1.781241e+00 -6.700736e-01 -9.590645e-02
## threshold_zoffset[123] -1.983073e+00 -6.573291e-01 -2.442498e-02
## threshold_zoffset[124] -1.582238e+00 -3.479265e-01  3.273912e-01
## threshold_zoffset[125] -1.585477e+00 -3.242609e-01  3.486562e-01
## threshold_zoffset[126] -1.805640e+00 -3.994751e-01  2.248738e-01
## threshold_zoffset[127] -1.529567e+00 -2.774501e-01  3.987489e-01
## threshold_zoffset[128] -2.132627e+00 -7.660845e-01 -9.545843e-02
## threshold_zoffset[129] -2.220936e+00 -1.118236e+00 -5.274382e-01
## threshold_zoffset[130] -1.766432e+00 -3.329036e-01  3.163781e-01
## threshold_zoffset[131] -1.826409e+00 -6.121958e-01 -2.289991e-02
## threshold_zoffset[132] -1.695965e+00 -4.359935e-01  2.422140e-01
## threshold_zoffset[133] -1.951500e+00 -7.791335e-01 -1.165353e-01
## threshold_zoffset[134] -1.632425e+00 -3.705372e-01  3.073783e-01
## threshold_zoffset[135] -1.958542e+00 -6.800513e-01  3.472242e-03
## threshold_zoffset[136] -1.654614e+00 -3.605292e-01  3.317950e-01
## threshold_zoffset[137] -1.904785e+00 -7.457253e-01 -1.048895e-01
## threshold_zoffset[138] -1.695213e+00 -3.963623e-01  2.332885e-01
## threshold_zoffset[139] -1.572385e+00 -2.066143e-01  4.660529e-01
## threshold_zoffset[140] -2.099452e+00 -7.896315e-01 -1.266033e-01
## threshold_zoffset[141] -1.862407e+00 -6.057912e-01  3.513842e-02
## threshold_zoffset[142] -1.628328e+00 -4.344323e-01  1.977933e-01
## threshold_zoffset[143] -1.685729e+00 -4.094691e-01  1.719143e-01
## threshold_zoffset[144] -1.775966e+00 -4.146448e-01  2.189406e-01
## threshold_zoffset[145] -1.743203e+00 -6.396144e-01  1.785030e-02
## threshold_zoffset[146] -1.723018e+00 -3.192522e-01  2.932881e-01
## threshold_zoffset[147] -2.744077e+00 -1.602360e+00 -9.652046e-01
## threshold_zoffset[148] -1.716098e+00 -5.431293e-01  1.052742e-01
## threshold_zoffset[149] -2.227762e+00 -9.949480e-01 -3.919055e-01
## threshold_zoffset[150] -1.925711e+00 -7.756488e-01 -1.365999e-01
## spread_zoffset[1]      -1.600438e+00 -3.120441e-01  3.944383e-01
## spread_zoffset[2]      -1.352400e+00 -7.217208e-02  4.988869e-01
## spread_zoffset[3]      -1.559659e+00 -4.719100e-01  1.147224e-01
## spread_zoffset[4]      -9.967571e-01  1.392426e-01  6.498129e-01
## spread_zoffset[5]      -1.403317e+00 -1.977776e-01  4.578850e-01
## spread_zoffset[6]      -2.343250e+00 -1.275434e+00 -7.762522e-01
## spread_zoffset[7]      -1.067730e+00 -3.140386e-02  5.152684e-01
## spread_zoffset[8]      -1.697085e+00 -2.380862e-01  5.039576e-01
## spread_zoffset[9]      -2.355580e+00 -1.395510e+00 -8.639824e-01
## spread_zoffset[10]     -1.265952e+00 -1.880655e-02  7.181359e-01
## spread_zoffset[11]     -1.880227e+00 -7.027203e-01 -5.597234e-02
## spread_zoffset[12]     -2.024507e+00 -9.441322e-01 -4.188050e-01
## spread_zoffset[13]     -2.063770e+00 -9.925336e-01 -4.612663e-01
## spread_zoffset[14]     -2.052142e+00 -7.656956e-01 -6.256879e-02
## spread_zoffset[15]     -1.328185e+00 -3.808782e-03  6.658964e-01
## spread_zoffset[16]     -2.244065e+00 -1.312657e+00 -7.902450e-01
## spread_zoffset[17]     -1.782219e+00 -4.864712e-01  1.241268e-01
## spread_zoffset[18]     -2.131126e+00 -1.084975e+00 -5.542284e-01
## spread_zoffset[19]     -1.909417e+00 -6.529305e-01 -8.264337e-03
## spread_zoffset[20]     -1.463089e+00 -4.661116e-01  1.089585e-02
## spread_zoffset[21]     -1.069111e+00 -4.443236e-02  4.523688e-01
## spread_zoffset[22]     -1.699507e+00 -7.589831e-01 -2.747160e-01
## spread_zoffset[23]     -1.354343e+00 -2.303138e-01  2.919527e-01
## spread_zoffset[24]     -1.854429e+00 -6.771602e-01  1.650381e-02
## spread_zoffset[25]     -1.184150e+00  1.331083e-01  7.522226e-01
## spread_zoffset[26]     -1.691024e+00 -4.305071e-01  3.190390e-01
## spread_zoffset[27]     -1.560558e+00 -6.980840e-01 -2.373268e-01
## spread_zoffset[28]     -1.113422e+00  1.872928e-02  5.752602e-01
## spread_zoffset[29]     -1.261441e+00 -2.696479e-01  2.167093e-01
## spread_zoffset[30]     -1.607354e+00 -3.477843e-01  3.171108e-01
## spread_zoffset[31]     -2.082068e+00 -1.051229e+00 -4.851295e-01
## spread_zoffset[32]     -1.688016e+00 -4.223316e-01  2.966133e-01
## spread_zoffset[33]     -1.074820e+00 -8.067176e-02  4.033031e-01
## spread_zoffset[34]     -1.528616e+00 -4.238745e-01  8.857943e-02
## spread_zoffset[35]     -1.855325e+00 -5.782455e-01 -6.301893e-02
## spread_zoffset[36]     -1.612408e+00 -6.410866e-01 -9.238596e-02
## spread_zoffset[37]     -1.549790e+00 -3.232499e-01  4.069268e-01
## spread_zoffset[38]     -1.270230e+00 -2.609999e-01  1.919982e-01
## spread_zoffset[39]     -1.464161e+00 -4.218463e-01  1.114522e-01
## spread_zoffset[40]     -2.185522e+00 -1.221124e+00 -7.221882e-01
## spread_zoffset[41]     -1.971508e+00 -6.815891e-01 -4.068841e-02
## spread_zoffset[42]     -1.654220e+00 -4.542602e-01  1.965348e-01
## spread_zoffset[43]     -1.719444e+00 -3.746091e-01  4.079358e-01
## spread_zoffset[44]     -1.583265e+00 -6.576503e-01 -1.221652e-01
## spread_zoffset[45]     -1.946546e+00 -9.498358e-01 -3.877569e-01
## spread_zoffset[46]     -1.978046e+00 -7.274417e-01 -4.055707e-02
## spread_zoffset[47]     -2.771230e+00 -1.714753e+00 -1.205897e+00
## spread_zoffset[48]     -1.902099e+00 -8.762321e-01 -3.446854e-01
## spread_zoffset[49]     -2.120696e+00 -1.127083e+00 -5.699554e-01
## spread_zoffset[50]     -1.624528e+00 -2.018752e-01  4.408874e-01
## spread_zoffset[51]     -1.350699e+00  1.455517e-03  5.792093e-01
## spread_zoffset[52]     -9.103730e-01  2.128993e-01  7.139909e-01
## spread_zoffset[53]     -2.435742e+00 -1.302621e+00 -7.109826e-01
## spread_zoffset[54]     -1.788913e+00 -7.310300e-01 -1.844778e-01
## spread_zoffset[55]     -1.453687e+00 -4.993017e-01 -3.723558e-03
## spread_zoffset[56]     -2.453974e+00 -1.366697e+00 -8.103181e-01
## spread_zoffset[57]     -2.204241e+00 -1.177010e+00 -6.608635e-01
## spread_zoffset[58]     -2.228810e+00 -1.177459e+00 -6.769249e-01
## spread_zoffset[59]     -9.892703e-01  5.312419e-02  5.414645e-01
## spread_zoffset[60]     -1.416163e+00 -2.037816e-01  4.363338e-01
## spread_zoffset[61]     -1.161152e+00 -1.820121e-01  2.846506e-01
## spread_zoffset[62]     -2.294311e+00 -1.070899e+00 -3.917341e-01
## spread_zoffset[63]     -1.221456e+00  2.261715e-02  5.649820e-01
## spread_zoffset[64]     -1.106331e+00  1.399765e-01  6.857045e-01
## spread_zoffset[65]     -8.319342e-01  1.307272e-01  6.062973e-01
## spread_zoffset[66]     -1.336926e+00 -1.545775e-01  3.604571e-01
## spread_zoffset[67]     -2.173710e+00 -1.191532e+00 -6.553010e-01
## spread_zoffset[68]     -1.849602e+00 -5.971617e-01  7.102430e-02
## spread_zoffset[69]     -2.980006e+00 -1.909560e+00 -1.392474e+00
## spread_zoffset[70]     -1.679015e+00 -5.312239e-01  3.823931e-02
## spread_zoffset[71]     -1.265778e+00 -3.522191e-02  5.766536e-01
## spread_zoffset[72]     -1.570277e+00 -3.037264e-01  3.655725e-01
## spread_zoffset[73]     -1.713943e+00 -5.402286e-01  1.074320e-01
## spread_zoffset[74]     -1.535629e+00 -5.109684e-01 -5.064556e-03
## spread_zoffset[75]     -1.226541e+00 -1.905640e-01  2.614497e-01
## spread_zoffset[76]     -1.841142e+00 -6.517596e-01  3.946764e-02
## spread_zoffset[77]     -3.282803e+00 -2.264001e+00 -1.710914e+00
## spread_zoffset[78]     -1.807822e+00 -8.669614e-01 -3.732862e-01
## spread_zoffset[79]     -1.464317e+00 -2.819258e-01  2.405909e-01
## spread_zoffset[80]     -1.620246e+00 -3.934740e-01  2.870601e-01
## spread_zoffset[81]     -1.562150e+00 -4.842827e-01  1.293609e-01
## spread_zoffset[82]     -1.068681e+00 -4.005915e-02  4.927577e-01
## spread_zoffset[83]     -1.731395e+00 -6.962759e-01 -1.935349e-01
## spread_zoffset[84]     -2.510695e+00 -1.497553e+00 -9.360307e-01
## spread_zoffset[85]     -2.582175e+00 -1.599470e+00 -1.038390e+00
## spread_zoffset[86]     -2.103105e+00 -1.018827e+00 -3.843474e-01
## spread_zoffset[87]     -1.918755e+00 -5.642080e-01  2.052556e-01
## spread_zoffset[88]     -1.184982e+00 -1.866933e-01  3.530417e-01
## spread_zoffset[89]     -1.500176e+00 -2.702998e-01  4.137541e-01
## spread_zoffset[90]     -7.996866e-01  4.298372e-01  9.838305e-01
## spread_zoffset[91]     -2.215255e+00 -1.180261e+00 -6.887798e-01
## spread_zoffset[92]     -1.205123e+00 -1.804212e-01  3.167018e-01
## spread_zoffset[93]     -1.626526e+00 -2.941670e-01  3.796418e-01
## spread_zoffset[94]     -1.945212e+00 -6.379477e-01  4.499975e-02
## spread_zoffset[95]     -1.367083e+00 -2.407748e-01  2.422460e-01
## spread_zoffset[96]     -1.944161e+00 -7.416366e-01  4.622970e-02
## spread_zoffset[97]     -1.910383e+00 -5.689295e-01  1.570583e-01
## spread_zoffset[98]     -2.670438e+00 -1.516404e+00 -9.835310e-01
## spread_zoffset[99]     -1.043086e+00  1.127762e-01  6.421574e-01
## spread_zoffset[100]    -1.146561e+00 -1.812428e-01  3.097533e-01
## spread_zoffset[101]    -1.040624e+00  3.893106e-01  1.049285e+00
## spread_zoffset[102]    -1.780139e+00 -8.330894e-01 -3.118091e-01
## spread_zoffset[103]    -1.867026e+00 -5.130332e-01  1.522942e-01
## spread_zoffset[104]    -1.902956e+00 -7.261792e-01 -1.870527e-01
## spread_zoffset[105]    -1.672230e+00 -5.011030e-01  4.314446e-02
## spread_zoffset[106]    -1.265042e+00 -4.822983e-02  5.255871e-01
## spread_zoffset[107]    -1.067358e+00  2.284957e-01  8.012334e-01
## spread_zoffset[108]    -1.504725e+00 -4.435901e-01  6.237506e-02
## spread_zoffset[109]    -1.569876e+00 -5.179925e-01 -4.052531e-02
## spread_zoffset[110]    -1.575505e+00 -2.463712e-01  4.630994e-01
## spread_zoffset[111]    -1.708353e+00 -7.662495e-01 -2.770350e-01
## spread_zoffset[112]    -1.754274e+00 -7.556108e-01 -2.383742e-01
## spread_zoffset[113]    -2.022286e+00 -9.474264e-01 -4.598632e-01
## spread_zoffset[114]    -1.705470e+00 -4.206187e-01  3.076868e-01
## spread_zoffset[115]    -1.556766e+00 -5.907640e-01 -4.560582e-02
## spread_zoffset[116]    -1.799397e+00 -8.022584e-01 -2.845363e-01
## spread_zoffset[117]    -1.512260e+00 -2.601533e-01  3.207615e-01
## spread_zoffset[118]    -1.820345e+00 -4.868986e-01  2.464842e-01
## spread_zoffset[119]    -1.892594e+00 -8.096767e-01 -3.295424e-01
## spread_zoffset[120]    -8.718151e-01  1.774670e-01  6.341603e-01
## spread_zoffset[121]    -1.807458e+00 -7.714093e-01 -2.815942e-01
## spread_zoffset[122]    -2.211284e+00 -1.280492e+00 -8.066146e-01
## spread_zoffset[123]    -1.738539e+00 -7.701856e-01 -2.929604e-01
## spread_zoffset[124]    -1.080208e+00 -1.598150e-01  3.111001e-01
## spread_zoffset[125]    -1.412982e+00 -4.477881e-01 -3.664086e-04
## spread_zoffset[126]    -1.734154e+00 -4.184829e-01  2.807407e-01
## spread_zoffset[127]    -1.261221e+00  1.317099e-01  6.787870e-01
## spread_zoffset[128]    -2.178610e+00 -9.088993e-01 -2.462598e-01
## spread_zoffset[129]    -2.304121e+00 -1.250992e+00 -7.218011e-01
## spread_zoffset[130]    -1.032508e+00  5.898734e-02  6.062227e-01
## spread_zoffset[131]    -2.109862e+00 -1.106385e+00 -5.942605e-01
## spread_zoffset[132]    -1.737000e+00 -3.381315e-01  3.739843e-01
## spread_zoffset[133]    -1.950597e+00 -9.387781e-01 -4.127933e-01
## spread_zoffset[134]    -1.192067e+00 -1.915981e-01  3.048137e-01
## spread_zoffset[135]    -2.012128e+00 -7.570900e-01 -8.670911e-02
## spread_zoffset[136]    -6.707478e-01  2.954952e-01  8.257395e-01
## spread_zoffset[137]    -1.968401e+00 -9.370062e-01 -4.020266e-01
## spread_zoffset[138]    -1.683348e+00 -6.363847e-01 -1.404250e-01
## spread_zoffset[139]    -1.203235e+00 -1.666850e-01  3.256672e-01
## spread_zoffset[140]    -2.103137e+00 -1.149324e+00 -6.133480e-01
## spread_zoffset[141]    -1.348167e+00 -7.264292e-02  4.795102e-01
## spread_zoffset[142]    -2.255675e+00 -9.990199e-01 -2.186061e-01
## spread_zoffset[143]    -1.922142e+00 -9.441635e-01 -3.867895e-01
## spread_zoffset[144]    -1.536280e+00 -3.688690e-01  1.821268e-01
## spread_zoffset[145]    -1.830814e+00 -4.849875e-01  2.556775e-01
## spread_zoffset[146]    -1.808532e+00 -5.074061e-01  1.393376e-01
## spread_zoffset[147]    -3.082883e+00 -2.018515e+00 -1.436622e+00
## spread_zoffset[148]    -1.675388e+00 -4.071748e-01  2.522456e-01
## spread_zoffset[149]    -1.840379e+00 -9.235098e-01 -4.124913e-01
## spread_zoffset[150]    -1.962223e+00 -9.756549e-01 -4.631290e-01
## lapse_zoffset[1]        3.947494e-01  1.018993e+00  1.234677e+00
## lapse_zoffset[2]       -1.928159e+00 -6.226423e-01  6.043027e-02
## lapse_zoffset[3]       -1.516462e+00 -2.469390e-01  2.023328e-01
## lapse_zoffset[4]       -1.963552e+00 -9.046061e-01 -3.221304e-01
## lapse_zoffset[5]       -1.576761e+00 -2.399173e-01  2.643812e-01
## lapse_zoffset[6]       -2.153414e+00 -1.049639e+00 -5.097083e-01
## lapse_zoffset[7]       -2.020907e+00 -6.927743e-01 -9.313259e-02
## lapse_zoffset[8]       -1.382701e+00  2.229503e-01  5.908277e-01
## lapse_zoffset[9]       -2.179793e+00 -1.106958e+00 -5.814113e-01
## lapse_zoffset[10]      -1.337004e+00  4.295130e-01  8.234463e-01
## lapse_zoffset[11]      -1.572011e+00 -1.260096e-01  3.703405e-01
## lapse_zoffset[12]      -2.076611e+00 -1.035712e+00 -5.120796e-01
## lapse_zoffset[13]      -2.098263e+00 -1.058876e+00 -5.638126e-01
## lapse_zoffset[14]       8.878914e-01  1.239414e+00  1.404919e+00
## lapse_zoffset[15]      -1.623122e+00 -1.342425e-01  4.726802e-01
## lapse_zoffset[16]      -2.316808e+00 -1.210124e+00 -6.522373e-01
## lapse_zoffset[17]      -1.876627e+00 -7.187222e-01 -1.408152e-01
## lapse_zoffset[18]      -2.066138e+00 -1.097985e+00 -5.310457e-01
## lapse_zoffset[19]       1.460254e+00  1.752474e+00  1.930255e+00
## lapse_zoffset[20]      -2.184793e+00 -1.056677e+00 -4.700172e-01
## lapse_zoffset[21]      -2.013153e+00 -8.645187e-01 -3.113070e-01
## lapse_zoffset[22]      -2.230902e+00 -1.122020e+00 -6.237165e-01
## lapse_zoffset[23]      -2.066728e+00 -7.030121e-01 -1.183650e-01
## lapse_zoffset[24]       1.617487e+00  1.922660e+00  2.106036e+00
## lapse_zoffset[25]      -1.547887e+00 -5.410697e-02  5.199415e-01
## lapse_zoffset[26]      -1.398061e+00  5.931798e-02  5.395164e-01
## lapse_zoffset[27]      -2.170668e+00 -1.018580e+00 -4.860681e-01
## lapse_zoffset[28]      -1.851977e+00 -5.921265e-01  2.666561e-02
## lapse_zoffset[29]      -2.002639e+00 -9.073457e-01 -3.704453e-01
## lapse_zoffset[30]      -4.682467e-01  7.803135e-01  1.027605e+00
## lapse_zoffset[31]      -2.205932e+00 -1.046491e+00 -4.759601e-01
## lapse_zoffset[32]       2.618267e-01  1.020985e+00  1.234419e+00
## lapse_zoffset[33]      -2.158409e+00 -9.191710e-01 -3.782117e-01
## lapse_zoffset[34]      -2.054106e+00 -8.240851e-01 -2.739552e-01
## lapse_zoffset[35]      -2.037757e+00 -8.894092e-01 -3.017795e-01
## lapse_zoffset[36]      -2.097120e+00 -1.023898e+00 -4.607459e-01
## lapse_zoffset[37]       6.814237e-01  1.211979e+00  1.421899e+00
## lapse_zoffset[38]      -2.180551e+00 -9.110376e-01 -3.124767e-01
## lapse_zoffset[39]      -2.057644e+00 -9.417699e-01 -4.300731e-01
## lapse_zoffset[40]      -2.112232e+00 -1.132994e+00 -6.210592e-01
## lapse_zoffset[41]      -1.808357e+00 -4.679186e-01  9.649899e-02
## lapse_zoffset[42]       1.033788e+00  1.345813e+00  1.505074e+00
## lapse_zoffset[43]      -1.359597e+00  3.477356e-01  7.698269e-01
## lapse_zoffset[44]      -2.117141e+00 -9.842939e-01 -4.306773e-01
## lapse_zoffset[45]      -2.129720e+00 -1.032252e+00 -5.262519e-01
## lapse_zoffset[46]       1.589227e+00  1.881958e+00  2.057492e+00
## lapse_zoffset[47]      -2.252315e+00 -1.191544e+00 -7.263298e-01
## lapse_zoffset[48]      -2.253460e+00 -1.097607e+00 -5.289168e-01
## lapse_zoffset[49]      -2.260183e+00 -1.091813e+00 -6.013009e-01
## lapse_zoffset[50]       1.021644e+00  1.328413e+00  1.494408e+00
## lapse_zoffset[51]      -2.008228e+00 -7.318750e-01 -1.427390e-01
## lapse_zoffset[52]      -1.920016e+00 -7.070750e-01 -2.001278e-02
## lapse_zoffset[53]      -2.163395e+00 -1.056759e+00 -5.082627e-01
## lapse_zoffset[54]      -1.971647e+00 -9.485396e-01 -4.501817e-01
## lapse_zoffset[55]      -2.180485e+00 -1.010601e+00 -4.469549e-01
## lapse_zoffset[56]      -2.089770e+00 -1.111044e+00 -5.942683e-01
## lapse_zoffset[57]      -2.317552e+00 -1.204555e+00 -6.677557e-01
## lapse_zoffset[58]      -2.152277e+00 -1.112427e+00 -5.571719e-01
## lapse_zoffset[59]      -2.080213e+00 -8.262245e-01 -2.571155e-01
## lapse_zoffset[60]      -1.407093e+00 -1.054492e-01  3.895094e-01
## lapse_zoffset[61]      -2.023417e+00 -9.241019e-01 -4.075161e-01
## lapse_zoffset[62]      -1.583583e+00 -4.430497e-01  1.216241e-02
## lapse_zoffset[63]      -1.730981e+00 -5.968408e-01 -2.632608e-02
## lapse_zoffset[64]      -1.713615e+00 -3.435156e-01  1.933924e-01
## lapse_zoffset[65]      -2.121395e+00 -9.788283e-01 -4.206519e-01
## lapse_zoffset[66]      -1.939209e+00 -6.755746e-01 -6.147535e-02
## lapse_zoffset[67]      -2.287809e+00 -1.163346e+00 -6.313017e-01
## lapse_zoffset[68]      -9.446192e-01  5.133844e-01  8.109702e-01
## lapse_zoffset[69]      -2.144672e+00 -1.083825e+00 -6.062011e-01
## lapse_zoffset[70]      -2.018046e+00 -9.055559e-01 -3.596220e-01
## lapse_zoffset[71]      -1.754256e+00 -3.608455e-01  2.209187e-01
## lapse_zoffset[72]       1.187883e+00  1.539258e+00  1.711990e+00
## lapse_zoffset[73]      -1.706956e+00 -4.532124e-01  3.739087e-02
## lapse_zoffset[74]      -2.076652e+00 -9.839801e-01 -4.624059e-01
## lapse_zoffset[75]      -2.108384e+00 -9.758738e-01 -4.185347e-01
## lapse_zoffset[76]      -1.546126e+00 -1.225972e-01  3.797846e-01
## lapse_zoffset[77]      -2.175246e+00 -1.177843e+00 -6.526346e-01
## lapse_zoffset[78]      -2.124585e+00 -1.016972e+00 -4.781291e-01
## lapse_zoffset[79]      -2.038678e+00 -9.276115e-01 -3.591445e-01
## lapse_zoffset[80]      -1.419040e+00 -1.270005e-01  3.555674e-01
## lapse_zoffset[81]      -1.770500e+00 -5.373276e-01 -5.770115e-02
## lapse_zoffset[82]      -2.124373e+00 -7.305598e-01 -1.269669e-01
## lapse_zoffset[83]      -2.100695e+00 -1.033676e+00 -5.046524e-01
## lapse_zoffset[84]      -2.126973e+00 -1.109428e+00 -5.678436e-01
## lapse_zoffset[85]      -2.246265e+00 -1.085210e+00 -5.786974e-01
## lapse_zoffset[86]       1.924947e-02  7.281317e-01  9.530622e-01
## lapse_zoffset[87]      -4.619047e-01  8.454791e-01  1.118235e+00
## lapse_zoffset[88]      -1.993808e+00 -8.343840e-01 -2.479401e-01
## lapse_zoffset[89]      -1.193325e+00  1.450673e-01  5.677912e-01
## lapse_zoffset[90]      -1.837223e+00 -4.575584e-01  2.078601e-01
## lapse_zoffset[91]      -2.317258e+00 -1.103327e+00 -5.373266e-01
## lapse_zoffset[92]      -1.994267e+00 -8.388009e-01 -2.682042e-01
## lapse_zoffset[93]      -1.151278e+00  4.916556e-01  8.215239e-01
## lapse_zoffset[94]       1.011485e+00  1.342421e+00  1.504212e+00
## lapse_zoffset[95]      -2.154236e+00 -9.497847e-01 -4.061781e-01
## lapse_zoffset[96]       1.155625e-01  9.816500e-01  1.196107e+00
## lapse_zoffset[97]       1.456669e+00  1.748449e+00  1.923443e+00
## lapse_zoffset[98]      -2.307052e+00 -1.215512e+00 -6.751710e-01
## lapse_zoffset[99]      -2.035158e+00 -7.088305e-01 -4.458883e-02
## lapse_zoffset[100]     -2.130454e+00 -9.308732e-01 -3.412101e-01
## lapse_zoffset[101]     -1.496645e+00 -7.898089e-02  4.442207e-01
## lapse_zoffset[102]     -2.314287e+00 -1.088338e+00 -5.512061e-01
## lapse_zoffset[103]      1.194445e+00  1.480649e+00  1.655531e+00
## lapse_zoffset[104]     -2.182969e+00 -9.925095e-01 -4.084660e-01
## lapse_zoffset[105]     -2.002799e+00 -8.438503e-01 -3.020723e-01
## lapse_zoffset[106]     -1.605450e+00 -3.755799e-01  1.726428e-01
## lapse_zoffset[107]     -2.027202e+00 -7.308654e-01 -1.263391e-01
## lapse_zoffset[108]     -2.045719e+00 -9.888317e-01 -4.796535e-01
## lapse_zoffset[109]     -2.191535e+00 -1.004788e+00 -4.325846e-01
## lapse_zoffset[110]      2.743600e-02  9.436741e-01  1.171849e+00
## lapse_zoffset[111]     -2.277216e+00 -1.055113e+00 -4.589309e-01
## lapse_zoffset[112]     -2.203162e+00 -1.038924e+00 -5.319016e-01
## lapse_zoffset[113]     -2.227849e+00 -1.100427e+00 -5.813119e-01
## lapse_zoffset[114]     -8.444234e-02  8.866046e-01  1.157789e+00
## lapse_zoffset[115]     -2.194734e+00 -1.027932e+00 -5.035910e-01
## lapse_zoffset[116]     -2.236952e+00 -9.687567e-01 -4.195371e-01
## lapse_zoffset[117]     -1.449952e+00 -1.703625e-01  3.216850e-01
## lapse_zoffset[118]      8.189743e-01  1.261335e+00  1.443205e+00
## lapse_zoffset[119]     -2.147275e+00 -1.022849e+00 -5.503169e-01
## lapse_zoffset[120]     -2.016174e+00 -9.546331e-01 -3.679183e-01
## lapse_zoffset[121]     -2.256230e+00 -1.061400e+00 -5.823967e-01
## lapse_zoffset[122]     -2.196770e+00 -1.029894e+00 -4.971672e-01
## lapse_zoffset[123]     -2.158437e+00 -1.020894e+00 -4.716398e-01
## lapse_zoffset[124]     -2.144214e+00 -9.103895e-01 -3.410332e-01
## lapse_zoffset[125]     -2.197900e+00 -1.029025e+00 -4.517640e-01
## lapse_zoffset[126]     -1.425224e+00  1.547340e-01  6.209025e-01
## lapse_zoffset[127]     -1.745267e+00 -3.865903e-01  2.442427e-01
## lapse_zoffset[128]      8.983390e-01  1.292524e+00  1.478936e+00
## lapse_zoffset[129]     -2.186965e+00 -1.112194e+00 -5.624777e-01
## lapse_zoffset[130]     -1.885397e+00 -5.910675e-01  1.644106e-02
## lapse_zoffset[131]     -2.078088e+00 -9.798771e-01 -4.687371e-01
## lapse_zoffset[132]     -8.580367e-01  4.794476e-01  7.810829e-01
## lapse_zoffset[133]     -2.296737e+00 -1.093269e+00 -5.622871e-01
## lapse_zoffset[134]     -2.088958e+00 -9.357073e-01 -3.222833e-01
## lapse_zoffset[135]      1.391122e+00  1.687986e+00  1.853502e+00
## lapse_zoffset[136]     -2.032515e+00 -8.133093e-01 -2.305345e-01
## lapse_zoffset[137]     -2.084497e+00 -9.793386e-01 -4.478057e-01
## lapse_zoffset[138]     -2.093041e+00 -9.283479e-01 -4.069956e-01
## lapse_zoffset[139]     -2.128480e+00 -8.576969e-01 -2.608065e-01
## lapse_zoffset[140]     -2.287320e+00 -1.112382e+00 -5.236536e-01
## lapse_zoffset[141]     -2.014061e+00 -7.444282e-01 -1.146002e-01
## lapse_zoffset[142]     -1.060320e+00  3.250459e-01  6.828431e-01
## lapse_zoffset[143]     -2.194498e+00 -1.059124e+00 -5.047569e-01
## lapse_zoffset[144]     -1.904372e+00 -5.769570e-01 -2.823085e-02
## lapse_zoffset[145]     -8.441908e-01  4.837999e-01  7.762898e-01
## lapse_zoffset[146]     -1.331396e+00  1.388618e-01  5.745322e-01
## lapse_zoffset[147]     -2.227095e+00 -1.219303e+00 -7.204623e-01
## lapse_zoffset[148]     -1.004425e+00  3.369353e-01  6.882381e-01
## lapse_zoffset[149]     -2.166143e+00 -1.029893e+00 -5.240935e-01
## lapse_zoffset[150]     -2.204334e+00 -1.041394e+00 -4.940344e-01
## threshold[1]            2.015446e+00  2.417360e+00  2.579557e+00
## threshold[2]            1.902994e+00  2.262482e+00  2.414378e+00
## threshold[3]            1.817073e+00  2.197688e+00  2.364115e+00
## threshold[4]            1.845751e+00  2.205722e+00  2.371228e+00
## threshold[5]            1.792519e+00  2.173234e+00  2.354061e+00
## threshold[6]            1.769580e+00  2.136080e+00  2.292127e+00
## threshold[7]            1.916951e+00  2.275364e+00  2.439775e+00
## threshold[8]            1.747853e+00  2.143851e+00  2.319228e+00
## threshold[9]            1.908053e+00  2.275860e+00  2.443406e+00
## threshold[10]           1.812416e+00  2.214965e+00  2.385812e+00
## threshold[11]           1.877976e+00  2.231471e+00  2.389406e+00
## threshold[12]           1.863815e+00  2.205034e+00  2.359575e+00
## threshold[13]           1.988869e+00  2.375202e+00  2.548107e+00
## threshold[14]           1.741130e+00  2.153859e+00  2.331935e+00
## threshold[15]           1.963547e+00  2.305711e+00  2.461815e+00
## threshold[16]           1.753725e+00  2.116446e+00  2.283233e+00
## threshold[17]           1.818624e+00  2.184609e+00  2.340326e+00
## threshold[18]           1.839730e+00  2.240644e+00  2.420962e+00
## threshold[19]           1.942941e+00  2.384807e+00  2.556255e+00
## threshold[20]           2.022971e+00  2.401778e+00  2.555789e+00
## threshold[21]           1.902435e+00  2.211527e+00  2.385821e+00
## threshold[22]           1.787469e+00  2.135916e+00  2.298963e+00
## threshold[23]           1.938798e+00  2.307510e+00  2.456930e+00
## threshold[24]           1.964732e+00  2.379265e+00  2.554218e+00
## threshold[25]           2.129882e+00  2.482234e+00  2.665920e+00
## threshold[26]           1.858542e+00  2.214452e+00  2.395711e+00
## threshold[27]           2.058855e+00  2.428627e+00  2.601150e+00
## threshold[28]           2.062775e+00  2.451424e+00  2.626446e+00
## threshold[29]           2.187921e+00  2.517767e+00  2.716048e+00
## threshold[30]           1.906327e+00  2.229734e+00  2.412794e+00
## threshold[31]           1.809056e+00  2.173205e+00  2.338597e+00
## threshold[32]           2.010586e+00  2.405142e+00  2.601319e+00
## threshold[33]           1.791212e+00  2.289426e+00  2.472559e+00
## threshold[34]           1.974672e+00  2.380263e+00  2.534478e+00
## threshold[35]           2.036319e+00  2.428393e+00  2.590361e+00
## threshold[36]           1.727193e+00  2.113643e+00  2.295628e+00
## threshold[37]           1.842233e+00  2.233312e+00  2.402165e+00
## threshold[38]           1.896587e+00  2.267515e+00  2.427275e+00
## threshold[39]           1.682807e+00  2.068595e+00  2.249858e+00
## threshold[40]           1.836638e+00  2.243928e+00  2.423495e+00
## threshold[41]           2.016564e+00  2.394404e+00  2.566487e+00
## threshold[42]           1.833629e+00  2.198540e+00  2.384998e+00
## threshold[43]           1.912106e+00  2.272137e+00  2.436101e+00
## threshold[44]           1.770989e+00  2.163606e+00  2.321743e+00
## threshold[45]           1.774522e+00  2.153590e+00  2.318286e+00
## threshold[46]           1.955202e+00  2.366770e+00  2.549839e+00
## threshold[47]           1.636296e+00  2.030553e+00  2.206032e+00
## threshold[48]           1.839221e+00  2.234105e+00  2.409853e+00
## threshold[49]           1.828804e+00  2.226442e+00  2.410685e+00
## threshold[50]           1.796543e+00  2.202441e+00  2.379737e+00
## threshold[51]           1.789054e+00  2.184123e+00  2.349823e+00
## threshold[52]           1.897180e+00  2.274886e+00  2.448164e+00
## threshold[53]           1.709326e+00  2.057290e+00  2.236578e+00
## threshold[54]           1.909683e+00  2.239345e+00  2.425331e+00
## threshold[55]           2.128071e+00  2.470074e+00  2.637017e+00
## threshold[56]           1.907253e+00  2.290025e+00  2.466817e+00
## threshold[57]           1.677547e+00  2.068384e+00  2.234967e+00
## threshold[58]           1.911030e+00  2.238837e+00  2.412559e+00
## threshold[59]           1.965240e+00  2.281223e+00  2.484532e+00
## threshold[60]           1.908230e+00  2.261262e+00  2.443285e+00
## threshold[61]           1.910070e+00  2.258551e+00  2.443781e+00
## threshold[62]           1.786924e+00  2.163236e+00  2.334221e+00
## threshold[63]           1.859105e+00  2.220114e+00  2.400706e+00
## threshold[64]           1.907195e+00  2.264802e+00  2.436048e+00
## threshold[65]           1.907403e+00  2.324596e+00  2.497438e+00
## threshold[66]           1.969624e+00  2.286210e+00  2.479299e+00
## threshold[67]           1.882218e+00  2.264980e+00  2.438810e+00
## threshold[68]           2.091591e+00  2.439537e+00  2.631802e+00
## threshold[69]           1.771043e+00  2.118590e+00  2.283781e+00
## threshold[70]           1.831355e+00  2.226679e+00  2.409581e+00
## threshold[71]           2.012772e+00  2.402716e+00  2.561002e+00
## threshold[72]           1.905634e+00  2.261378e+00  2.431204e+00
## threshold[73]           1.840631e+00  2.206399e+00  2.375129e+00
## threshold[74]           1.991528e+00  2.362798e+00  2.529715e+00
## threshold[75]           2.082024e+00  2.437143e+00  2.600962e+00
## threshold[76]           1.825401e+00  2.208289e+00  2.368731e+00
## threshold[77]           1.645020e+00  2.000880e+00  2.172503e+00
## threshold[78]           1.884761e+00  2.244187e+00  2.414640e+00
## threshold[79]           1.820715e+00  2.232404e+00  2.421641e+00
## threshold[80]           1.882950e+00  2.240587e+00  2.414282e+00
## threshold[81]           1.713437e+00  2.095336e+00  2.275590e+00
## threshold[82]           2.107141e+00  2.447320e+00  2.620331e+00
## threshold[83]           2.118676e+00  2.454405e+00  2.613695e+00
## threshold[84]           2.014350e+00  2.351151e+00  2.521971e+00
## threshold[85]           1.771042e+00  2.115364e+00  2.283451e+00
## threshold[86]           1.833346e+00  2.184481e+00  2.356222e+00
## threshold[87]           1.882177e+00  2.247499e+00  2.411754e+00
## threshold[88]           2.107403e+00  2.441049e+00  2.609184e+00
## threshold[89]           2.070665e+00  2.436947e+00  2.616551e+00
## threshold[90]           1.985242e+00  2.330786e+00  2.498547e+00
## threshold[91]           1.688398e+00  2.096209e+00  2.267550e+00
## threshold[92]           1.897081e+00  2.237862e+00  2.429711e+00
## threshold[93]           1.852120e+00  2.225805e+00  2.388443e+00
## threshold[94]           1.799405e+00  2.183163e+00  2.365737e+00
## threshold[95]           1.881576e+00  2.231840e+00  2.404259e+00
## threshold[96]           1.771461e+00  2.160849e+00  2.355787e+00
## threshold[97]           1.943644e+00  2.348506e+00  2.519075e+00
## threshold[98]           1.696683e+00  2.038780e+00  2.214831e+00
## threshold[99]           2.094659e+00  2.452987e+00  2.623899e+00
## threshold[100]          1.877892e+00  2.254653e+00  2.414411e+00
## threshold[101]          1.807416e+00  2.193854e+00  2.368673e+00
## threshold[102]          1.935381e+00  2.332064e+00  2.503168e+00
## threshold[103]          1.997325e+00  2.385745e+00  2.561229e+00
## threshold[104]          1.761282e+00  2.125653e+00  2.287347e+00
## threshold[105]          2.008624e+00  2.380419e+00  2.534912e+00
## threshold[106]          1.877043e+00  2.228345e+00  2.401268e+00
## threshold[107]          2.275637e+00  2.595545e+00  2.881193e+00
## threshold[108]          1.790613e+00  2.132291e+00  2.314098e+00
## threshold[109]          1.828579e+00  2.206261e+00  2.366571e+00
## threshold[110]          1.832674e+00  2.231965e+00  2.404148e+00
## threshold[111]          1.892056e+00  2.241810e+00  2.407323e+00
## threshold[112]          1.874870e+00  2.188584e+00  2.376195e+00
## threshold[113]          1.752582e+00  2.106702e+00  2.263066e+00
## threshold[114]          1.804642e+00  2.202157e+00  2.368261e+00
## threshold[115]          1.810681e+00  2.159427e+00  2.317696e+00
## threshold[116]          1.896911e+00  2.235775e+00  2.384454e+00
## threshold[117]          2.089173e+00  2.448989e+00  2.625567e+00
## threshold[118]          1.852019e+00  2.242847e+00  2.398429e+00
## threshold[119]          1.932906e+00  2.254970e+00  2.439741e+00
## threshold[120]          1.879835e+00  2.222633e+00  2.376187e+00
## threshold[121]          1.868844e+00  2.201227e+00  2.373424e+00
## threshold[122]          1.894382e+00  2.214416e+00  2.359777e+00
## threshold[123]          1.847608e+00  2.212778e+00  2.381928e+00
## threshold[124]          1.939666e+00  2.301472e+00  2.465051e+00
## threshold[125]          2.132935e+00  2.459851e+00  2.649852e+00
## threshold[126]          1.911578e+00  2.267235e+00  2.425976e+00
## threshold[127]          1.994336e+00  2.305184e+00  2.472508e+00
## threshold[128]          1.778969e+00  2.192722e+00  2.366646e+00
## threshold[129]          1.709995e+00  2.099303e+00  2.263870e+00
## threshold[130]          2.071304e+00  2.461843e+00  2.631535e+00
## threshold[131]          2.004660e+00  2.388780e+00  2.544884e+00
## threshold[132]          1.872130e+00  2.216157e+00  2.406980e+00
## threshold[133]          1.763585e+00  2.148179e+00  2.323661e+00
## threshold[134]          1.962168e+00  2.292251e+00  2.449114e+00
## threshold[135]          1.778810e+00  2.158757e+00  2.350027e+00
## threshold[136]          1.916399e+00  2.280586e+00  2.456415e+00
## threshold[137]          1.991524e+00  2.358843e+00  2.518931e+00
## threshold[138]          2.087539e+00  2.450724e+00  2.620376e+00
## threshold[139]          1.997746e+00  2.318352e+00  2.494528e+00
## threshold[140]          1.798104e+00  2.184135e+00  2.355861e+00
## threshold[141]          1.833808e+00  2.189791e+00  2.364469e+00
## threshold[142]          2.055153e+00  2.421451e+00  2.603107e+00
## threshold[143]          1.945528e+00  2.262564e+00  2.425261e+00
## threshold[144]          1.859000e+00  2.223312e+00  2.403990e+00
## threshold[145]          1.824930e+00  2.180300e+00  2.355674e+00
## threshold[146]          1.928151e+00  2.282201e+00  2.449351e+00
## threshold[147]          1.568069e+00  1.945455e+00  2.121726e+00
## threshold[148]          2.036339e+00  2.415065e+00  2.575399e+00
## threshold[149]          1.877868e+00  2.283673e+00  2.449972e+00
## threshold[150]          1.807765e+00  2.181014e+00  2.346126e+00
## spread[1]               1.003485e+00  1.430647e+00  1.711189e+00
## spread[2]               1.116350e+00  1.572439e+00  1.816267e+00
## spread[3]               1.048643e+00  1.414476e+00  1.658331e+00
## spread[4]               1.434557e+00  1.883901e+00  2.148127e+00
## spread[5]               1.242134e+00  1.727180e+00  2.043305e+00
## spread[6]               8.652277e-01  1.146284e+00  1.321033e+00
## spread[7]               1.210243e+00  1.591506e+00  1.825932e+00
## spread[8]               1.152902e+00  1.683080e+00  2.050222e+00
## spread[9]               7.895780e-01  1.074793e+00  1.255010e+00
## spread[10]              1.154325e+00  1.581368e+00  1.907708e+00
## spread[11]              9.369900e-01  1.336824e+00  1.583822e+00
## spread[12]              1.050329e+00  1.423645e+00  1.635976e+00
## spread[13]              9.153622e-01  1.205320e+00  1.388918e+00
## spread[14]              1.019977e+00  1.486061e+00  1.784998e+00
## spread[15]              1.079046e+00  1.585305e+00  1.906015e+00
## spread[16]              9.708629e-01  1.286084e+00  1.494571e+00
## spread[17]              9.622068e-01  1.425644e+00  1.663123e+00
## spread[18]              8.772734e-01  1.170440e+00  1.364269e+00
## spread[19]              9.019420e-01  1.314392e+00  1.560442e+00
## spread[20]              1.048118e+00  1.374708e+00  1.568547e+00
## spread[21]              1.376554e+00  1.796741e+00  2.037639e+00
## spread[22]              1.154765e+00  1.485057e+00  1.702885e+00
## spread[23]              1.088988e+00  1.499190e+00  1.736689e+00
## spread[24]              8.890022e-01  1.311387e+00  1.562990e+00
## spread[25]              1.103469e+00  1.615817e+00  1.891920e+00
## spread[26]              1.139069e+00  1.622827e+00  1.955754e+00
## spread[27]              1.009708e+00  1.303603e+00  1.471194e+00
## spread[28]              1.157692e+00  1.562365e+00  1.821103e+00
## spread[29]              1.116656e+00  1.450610e+00  1.643058e+00
## spread[30]              1.204637e+00  1.634502e+00  1.960844e+00
## spread[31]              9.316573e-01  1.216924e+00  1.411975e+00
## spread[32]              9.872595e-01  1.387706e+00  1.680806e+00
## spread[33]              1.161198e+00  1.519732e+00  1.732536e+00
## spread[34]              1.061164e+00  1.392554e+00  1.595386e+00
## spread[35]              9.633021e-01  1.341850e+00  1.531286e+00
## spread[36]              1.028123e+00  1.361019e+00  1.567087e+00
## spread[37]              1.029345e+00  1.479372e+00  1.770301e+00
## spread[38]              1.152728e+00  1.489055e+00  1.690330e+00
## spread[39]              1.222396e+00  1.619666e+00  1.885682e+00
## spread[40]              8.394574e-01  1.125304e+00  1.289178e+00
## spread[41]              9.204242e-01  1.305731e+00  1.546305e+00
## spread[42]              1.148208e+00  1.602865e+00  1.901472e+00
## spread[43]              9.924926e-01  1.454506e+00  1.774806e+00
## spread[44]              1.067031e+00  1.365845e+00  1.556704e+00
## spread[45]              1.066359e+00  1.435918e+00  1.646779e+00
## spread[46]              8.927948e-01  1.290575e+00  1.537705e+00
## spread[47]              8.091919e-01  1.145164e+00  1.341406e+00
## spread[48]              9.185297e-01  1.247004e+00  1.433207e+00
## spread[49]              8.926880e-01  1.149716e+00  1.341130e+00
## spread[50]              1.159715e+00  1.705716e+00  2.020380e+00
## spread[51]              1.276781e+00  1.822996e+00  2.114936e+00
## spread[52]              1.272336e+00  1.673452e+00  1.935407e+00
## spread[53]              9.455593e-01  1.296213e+00  1.512545e+00
## spread[54]              1.126532e+00  1.512932e+00  1.736723e+00
## spread[55]              1.059840e+00  1.358235e+00  1.559240e+00
## spread[56]              7.883205e-01  1.087688e+00  1.261612e+00
## spread[57]              9.890681e-01  1.336337e+00  1.536204e+00
## spread[58]              9.883727e-01  1.326464e+00  1.537936e+00
## spread[59]              1.392006e+00  1.816421e+00  2.088148e+00
## spread[60]              1.241989e+00  1.694479e+00  2.022908e+00
## spread[61]              1.370772e+00  1.722022e+00  1.965423e+00
## spread[62]              9.333131e-01  1.380980e+00  1.643273e+00
## spread[63]              1.289760e+00  1.812570e+00  2.125116e+00
## spread[64]              1.360407e+00  1.858998e+00  2.157694e+00
## spread[65]              1.251519e+00  1.597954e+00  1.823534e+00
## spread[66]              1.265710e+00  1.737843e+00  1.991438e+00
## spread[67]              8.732074e-01  1.138896e+00  1.322986e+00
## spread[68]              9.455115e-01  1.323698e+00  1.586153e+00
## spread[69]              6.876186e-01  9.596102e-01  1.130433e+00
## spread[70]              9.622540e-01  1.352725e+00  1.565091e+00
## spread[71]              1.120043e+00  1.529104e+00  1.796829e+00
## spread[72]              1.039018e+00  1.492168e+00  1.751725e+00
## spread[73]              1.130091e+00  1.569295e+00  1.856497e+00
## spread[74]              1.033929e+00  1.361525e+00  1.563889e+00
## spread[75]              1.137460e+00  1.479484e+00  1.669176e+00
## spread[76]              9.359552e-01  1.358892e+00  1.629117e+00
## spread[77]              6.007705e-01  8.723761e-01  1.030716e+00
## spread[78]              9.697015e-01  1.279663e+00  1.473679e+00
## spread[79]              1.059036e+00  1.449675e+00  1.655217e+00
## spread[80]              1.128012e+00  1.639840e+00  1.956557e+00
## spread[81]              1.179459e+00  1.599098e+00  1.875160e+00
## spread[82]              1.167565e+00  1.529737e+00  1.754914e+00
## spread[83]              9.817304e-01  1.300845e+00  1.488143e+00
## spread[84]              7.563903e-01  1.055755e+00  1.222616e+00
## spread[85]              7.592024e-01  1.050700e+00  1.233348e+00
## spread[86]              9.943764e-01  1.389898e+00  1.639654e+00
## spread[87]              9.526242e-01  1.370287e+00  1.669171e+00
## spread[88]              1.130610e+00  1.494808e+00  1.701014e+00
## spread[89]              1.035643e+00  1.448144e+00  1.713400e+00
## spread[90]              1.292092e+00  1.774382e+00  2.057045e+00
## spread[91]              8.516132e-01  1.175448e+00  1.347549e+00
## spread[92]              1.312337e+00  1.728547e+00  1.979494e+00
## spread[93]              1.035938e+00  1.472235e+00  1.764997e+00
## spread[94]              1.048329e+00  1.539676e+00  1.821650e+00
## spread[95]              1.166100e+00  1.508352e+00  1.706295e+00
## spread[96]              9.305274e-01  1.327072e+00  1.609481e+00
## spread[97]              9.176228e-01  1.340227e+00  1.618779e+00
## spread[98]              8.692047e-01  1.206561e+00  1.419334e+00
## spread[99]              1.188853e+00  1.594628e+00  1.828319e+00
## spread[100]             1.210493e+00  1.536367e+00  1.749161e+00
## spread[101]             1.372351e+00  1.977950e+00  2.389472e+00
## spread[102]             9.625553e-01  1.248570e+00  1.430207e+00
## spread[103]             9.077250e-01  1.354159e+00  1.620935e+00
## spread[104]             1.071453e+00  1.508915e+00  1.739456e+00
## spread[105]             9.802263e-01  1.368803e+00  1.576651e+00
## spread[106]             1.298587e+00  1.783113e+00  2.082979e+00
## spread[107]             1.157421e+00  1.633776e+00  1.920082e+00
## spread[108]             1.215193e+00  1.614819e+00  1.848442e+00
## spread[109]             1.053881e+00  1.396151e+00  1.593852e+00
## spread[110]             1.182253e+00  1.675535e+00  2.024930e+00
## spread[111]             1.021412e+00  1.310893e+00  1.496419e+00
## spread[112]             1.111218e+00  1.491710e+00  1.713482e+00
## spread[113]             1.041632e+00  1.408329e+00  1.622999e+00
## spread[114]             1.010609e+00  1.420997e+00  1.726630e+00
## spread[115]             1.064700e+00  1.384523e+00  1.580581e+00
## spread[116]             9.840157e-01  1.307838e+00  1.501553e+00
## spread[117]             1.023894e+00  1.437193e+00  1.672852e+00
## spread[118]             9.831963e-01  1.408882e+00  1.683724e+00
## spread[119]             1.110513e+00  1.469350e+00  1.672928e+00
## spread[120]             1.290623e+00  1.674824e+00  1.892842e+00
## spread[121]             1.135842e+00  1.488165e+00  1.688433e+00
## spread[122]             8.554827e-01  1.144960e+00  1.313931e+00
## spread[123]             1.028194e+00  1.313953e+00  1.485439e+00
## spread[124]             1.205100e+00  1.529054e+00  1.736256e+00
## spread[125]             1.061377e+00  1.382307e+00  1.552106e+00
## spread[126]             1.020484e+00  1.441443e+00  1.720752e+00
## spread[127]             1.155283e+00  1.639439e+00  1.914948e+00
## spread[128]             8.571550e-01  1.260105e+00  1.507658e+00
## spread[129]             8.751100e-01  1.152387e+00  1.336897e+00
## spread[130]             1.205553e+00  1.580243e+00  1.823439e+00
## spread[131]             8.718726e-01  1.151424e+00  1.333295e+00
## spread[132]             1.129722e+00  1.635842e+00  1.978983e+00
## spread[133]             1.073731e+00  1.431289e+00  1.639261e+00
## spread[134]             1.202453e+00  1.524448e+00  1.735579e+00
## spread[135]             1.029498e+00  1.498139e+00  1.778897e+00
## spread[136]             1.345736e+00  1.724832e+00  1.988598e+00
## spread[137]             9.234276e-01  1.224225e+00  1.410463e+00
## spread[138]             9.908901e-01  1.318942e+00  1.496152e+00
## spread[139]             1.196866e+00  1.534439e+00  1.753737e+00
## spread[140]             9.105375e-01  1.193126e+00  1.373024e+00
## spread[141]             1.261274e+00  1.771368e+00  2.054886e+00
## spread[142]             7.917322e-01  1.193855e+00  1.480833e+00
## spread[143]             9.661966e-01  1.261772e+00  1.452317e+00
## spread[144]             1.201460e+00  1.645244e+00  1.902913e+00
## spread[145]             1.109700e+00  1.588134e+00  1.932464e+00
## spread[146]             9.890363e-01  1.401872e+00  1.652143e+00
## spread[147]             7.395999e-01  1.052439e+00  1.265607e+00
## spread[148]             9.926537e-01  1.394217e+00  1.656599e+00
## spread[149]             9.480756e-01  1.227347e+00  1.393923e+00
## spread[150]             9.621937e-01  1.253194e+00  1.433384e+00
## lapse[1]                1.862806e-02  7.685073e-02  1.031480e-01
## lapse[2]                1.338580e-04  2.514337e-03  9.700088e-03
## lapse[3]                3.160492e-04  5.220687e-03  1.341203e-02
## lapse[4]                1.971069e-04  2.391477e-03  7.607194e-03
## lapse[5]                4.909504e-04  8.292307e-03  2.284962e-02
## lapse[6]                9.654459e-05  1.113309e-03  3.136737e-03
## lapse[7]                1.121081e-04  1.972007e-03  7.742765e-03
## lapse[8]                6.171119e-04  2.058655e-02  4.335979e-02
## lapse[9]                1.045154e-04  1.150315e-03  3.248251e-03
## lapse[10]               3.991871e-04  1.971607e-02  4.461387e-02
## lapse[11]               2.723164e-04  6.752498e-03  1.841728e-02
## lapse[12]               1.440165e-04  1.715254e-03  4.761348e-03
## lapse[13]               1.159124e-04  1.242629e-03  3.440108e-03
## lapse[14]               9.505213e-02  1.475934e-01  1.744357e-01
## lapse[15]               2.416834e-04  6.096375e-03  2.235444e-02
## lapse[16]               9.827976e-05  1.287495e-03  3.604929e-03
## lapse[17]               1.085617e-04  2.007489e-03  6.482874e-03
## lapse[18]               1.347784e-04  1.159971e-03  3.512811e-03
## lapse[19]               2.241605e-01  2.771021e-01  3.046910e-01
## lapse[20]               1.089038e-04  1.225493e-03  4.050120e-03
## lapse[21]               1.650123e-04  2.262622e-03  7.183850e-03
## lapse[22]               1.362121e-04  1.436182e-03  4.157442e-03
## lapse[23]               9.825347e-05  2.050983e-03  6.913714e-03
## lapse[24]               2.898946e-01  3.474464e-01  3.798539e-01
## lapse[25]               3.899245e-04  8.897656e-03  2.826352e-02
## lapse[26]               6.079860e-04  1.563292e-02  3.844180e-02
## lapse[27]               8.670530e-05  1.318659e-03  3.748326e-03
## lapse[28]               2.063673e-04  2.968271e-03  1.030534e-02
## lapse[29]               1.771731e-04  1.541366e-03  4.844242e-03
## lapse[30]               5.371612e-03  6.549939e-02  9.257691e-02
## lapse[31]               8.436602e-05  1.160332e-03  3.388248e-03
## lapse[32]               1.691988e-02  7.663291e-02  1.033199e-01
## lapse[33]               1.010285e-04  1.603724e-03  4.788128e-03
## lapse[34]               1.432645e-04  1.831564e-03  5.968115e-03
## lapse[35]               1.643119e-04  1.728987e-03  5.521313e-03
## lapse[36]               8.863038e-05  1.115952e-03  3.543479e-03
## lapse[37]               3.396759e-02  9.436839e-02  1.227799e-01
## lapse[38]               8.932090e-05  1.369005e-03  4.584789e-03
## lapse[39]               1.625303e-04  1.947349e-03  5.808058e-03
## lapse[40]               1.159081e-04  1.103071e-03  3.047022e-03
## lapse[41]               2.382751e-04  4.000365e-03  1.252020e-02
## lapse[42]               1.163313e-01  1.749524e-01  2.068451e-01
## lapse[43]               5.428410e-04  1.675542e-02  3.903915e-02
## lapse[44]               8.857251e-05  1.271598e-03  3.802717e-03
## lapse[45]               1.651857e-04  1.611397e-03  4.959311e-03
## lapse[46]               2.738234e-01  3.307950e-01  3.601106e-01
## lapse[47]               1.324566e-04  1.312124e-03  3.432336e-03
## lapse[48]               1.001053e-04  1.198990e-03  3.613711e-03
## lapse[49]               8.404685e-05  1.130343e-03  3.206820e-03
## lapse[50]               1.094658e-01  1.732893e-01  2.030255e-01
## lapse[51]               1.564021e-04  2.991576e-03  1.003994e-02
## lapse[52]               1.284649e-04  1.984520e-03  8.308575e-03
## lapse[53]               1.585016e-04  1.646485e-03  4.849302e-03
## lapse[54]               1.633338e-04  1.930653e-03  5.642764e-03
## lapse[55]               8.409044e-05  1.345611e-03  4.194530e-03
## lapse[56]               1.149408e-04  1.141508e-03  3.087619e-03
## lapse[57]               8.931156e-05  1.305733e-03  3.656386e-03
## lapse[58]               1.294304e-04  1.493912e-03  4.564614e-03
## lapse[59]               1.673908e-04  2.392483e-03  8.084363e-03
## lapse[60]               5.855828e-04  1.161389e-02  2.817972e-02
## lapse[61]               1.632041e-04  2.130865e-03  6.502528e-03
## lapse[62]               4.050010e-04  5.392964e-03  1.411595e-02
## lapse[63]               2.893607e-04  3.986764e-03  1.269279e-02
## lapse[64]               3.265945e-04  6.572363e-03  1.966209e-02
## lapse[65]               1.093831e-04  1.312900e-03  4.481642e-03
## lapse[66]               1.858574e-04  3.448270e-03  1.119829e-02
## lapse[67]               8.014590e-05  9.991442e-04  2.925887e-03
## lapse[68]               1.471444e-03  2.826011e-02  4.875798e-02
## lapse[69]               8.617233e-05  9.625368e-04  2.686692e-03
## lapse[70]               1.281635e-04  1.553727e-03  5.170802e-03
## lapse[71]               2.496988e-04  4.805774e-03  1.593789e-02
## lapse[72]               1.175933e-01  1.683990e-01  1.970302e-01
## lapse[73]               3.160771e-04  5.336802e-03  1.508131e-02
## lapse[74]               1.401791e-04  1.453475e-03  3.896204e-03
## lapse[75]               1.318694e-04  1.469581e-03  4.373331e-03
## lapse[76]               2.826305e-04  6.787184e-03  1.846716e-02
## lapse[77]               8.077324e-05  8.564736e-04  2.401979e-03
## lapse[78]               8.958576e-05  1.169512e-03  3.345699e-03
## lapse[79]               1.330888e-04  1.568685e-03  5.298265e-03
## lapse[80]               6.524055e-04  1.046614e-02  2.716744e-02
## lapse[81]               3.007886e-04  4.499835e-03  1.223385e-02
## lapse[82]               1.194469e-04  2.332570e-03  7.325438e-03
## lapse[83]               1.114058e-04  1.243722e-03  3.764072e-03
## lapse[84]               1.077154e-04  1.113650e-03  3.432138e-03
## lapse[85]               8.214161e-05  9.825729e-04  2.786454e-03
## lapse[86]               1.181673e-02  5.786912e-02  8.091580e-02
## lapse[87]               2.848502e-03  4.798434e-02  7.231502e-02
## lapse[88]               1.614019e-04  1.861343e-03  6.265490e-03
## lapse[89]               7.658773e-04  1.316425e-02  3.091526e-02
## lapse[90]               1.599114e-04  3.189582e-03  1.387713e-02
## lapse[91]               6.982380e-05  9.681621e-04  2.980274e-03
## lapse[92]               1.804090e-04  2.358479e-03  8.078499e-03
## lapse[93]               5.949610e-04  2.256946e-02  4.435555e-02
## lapse[94]               1.176400e-01  1.735612e-01  2.019976e-01
## lapse[95]               1.077887e-04  1.257238e-03  3.905043e-03
## lapse[96]               7.851800e-03  6.259003e-02  8.484765e-02
## lapse[97]               2.127347e-01  2.716302e-01  3.017465e-01
## lapse[98]               1.187972e-04  1.189099e-03  3.628395e-03
## lapse[99]               1.260436e-04  2.400352e-03  8.921718e-03
## lapse[100]              1.092670e-04  1.360155e-03  4.600223e-03
## lapse[101]              4.341203e-04  1.057921e-02  3.228107e-02
## lapse[102]              9.936642e-05  1.128050e-03  3.579170e-03
## lapse[103]              1.308642e-01  1.777911e-01  2.040431e-01
## lapse[104]              1.274173e-04  1.796906e-03  5.926595e-03
## lapse[105]              1.586155e-04  1.801392e-03  5.900426e-03
## lapse[106]              3.157125e-04  6.310197e-03  2.009147e-02
## lapse[107]              1.511605e-04  2.229166e-03  8.092793e-03
## lapse[108]              1.739688e-04  1.894076e-03  5.323654e-03
## lapse[109]              6.540011e-05  1.194999e-03  3.597850e-03
## lapse[110]              1.383554e-02  8.846264e-02  1.190447e-01
## lapse[111]              7.592497e-05  1.092919e-03  3.507261e-03
## lapse[112]              1.175810e-04  1.767334e-03  4.964840e-03
## lapse[113]              1.512114e-04  1.442208e-03  4.482276e-03
## lapse[114]              5.805784e-03  5.287524e-02  7.830018e-02
## lapse[115]              9.178905e-05  1.114517e-03  3.269562e-03
## lapse[116]              7.964445e-05  1.248574e-03  3.869812e-03
## lapse[117]              5.578390e-04  7.378691e-03  1.906361e-02
## lapse[118]              5.462989e-02  1.028546e-01  1.296731e-01
## lapse[119]              1.377531e-04  1.622860e-03  4.878493e-03
## lapse[120]              1.290705e-04  1.286455e-03  4.227164e-03
## lapse[121]              1.353838e-04  1.527653e-03  4.437809e-03
## lapse[122]              7.955778e-05  1.088537e-03  3.183720e-03
## lapse[123]              1.067037e-04  1.122734e-03  3.383523e-03
## lapse[124]              1.058276e-04  1.397226e-03  4.431948e-03
## lapse[125]              1.112852e-04  1.226405e-03  4.371321e-03
## lapse[126]              3.753190e-04  1.225391e-02  2.975008e-02
## lapse[127]              2.035298e-04  3.801046e-03  1.426358e-02
## lapse[128]              6.868599e-02  1.100640e-01  1.346118e-01
## lapse[129]              9.157421e-05  9.970844e-04  2.918003e-03
## lapse[130]              1.657591e-04  3.167976e-03  1.049768e-02
## lapse[131]              1.382229e-04  1.367689e-03  4.163384e-03
## lapse[132]              1.837265e-03  3.633608e-02  6.173944e-02
## lapse[133]              1.125981e-04  1.635744e-03  4.507122e-03
## lapse[134]              1.039115e-04  1.297856e-03  4.690335e-03
## lapse[135]              2.473833e-01  3.026066e-01  3.328702e-01
## lapse[136]              1.294819e-04  1.618248e-03  5.400168e-03
## lapse[137]              1.294842e-04  1.477317e-03  4.250563e-03
## lapse[138]              1.286747e-04  1.552450e-03  4.646570e-03
## lapse[139]              1.072463e-04  1.518602e-03  5.035239e-03
## lapse[140]              8.804912e-05  9.623558e-04  2.993641e-03
## lapse[141]              1.979886e-04  2.775041e-03  1.053927e-02
## lapse[142]              1.290526e-03  1.897683e-02  3.850032e-02
## lapse[143]              7.908669e-05  1.050180e-03  3.169748e-03
## lapse[144]              2.502124e-04  4.303049e-03  1.270996e-02
## lapse[145]              2.093406e-03  3.609933e-02  5.999529e-02
## lapse[146]              4.294001e-04  1.196582e-02  2.624900e-02
## lapse[147]              1.212909e-04  1.261087e-03  3.217014e-03
## lapse[148]              1.282098e-03  2.063016e-02  3.880061e-02
## lapse[149]              1.282137e-04  1.222558e-03  3.531850e-03
## lapse[150]              7.828616e-05  1.083608e-03  3.197566e-03
## lp__                   -6.523772e+03 -6.500023e+03 -6.486300e+03
##                                  75%         97.5%     n_eff      Rhat
## sigma_log_threshold     1.469579e-01  2.060819e-01  166.4705 1.0053572
## sigma_log_spread        2.982381e-01  3.785282e-01  188.1767 1.0152957
## sigma_logit_lapse       2.130261e+00  2.482343e+00  534.2332 1.0043465
## b_threshold[1]          9.758064e-01  1.030429e+00 1745.0463 0.9997879
## b_threshold[2]          9.020340e-01  9.687447e-01 2160.9429 0.9999632
## b_threshold[3]          9.004993e-01  9.681132e-01 1942.9611 0.9993030
## b_spread[1]             4.989232e-01  5.933792e-01 1323.7726 1.0029470
## b_spread[2]             5.358259e-01  6.355901e-01  506.9196 1.0047280
## b_spread[3]             6.615675e-01  7.845559e-01  626.7374 1.0055835
## b_lapse[1]             -4.326248e+00 -3.822421e+00  608.0269 1.0006736
## b_lapse[2]             -4.451679e+00 -3.891186e+00  405.8351 1.0018698
## b_lapse[3]             -4.008164e+00 -3.517492e+00  483.2393 1.0086742
## threshold_zoffset[1]    7.858541e-01  2.074654e+00 3609.5962 0.9996557
## threshold_zoffset[2]    7.742180e-01  1.931233e+00 3319.8144 0.9991405
## threshold_zoffset[3]    4.979258e-01  1.695896e+00 3467.4552 0.9997988
## threshold_zoffset[4]    6.689382e-01  1.788479e+00 2900.6591 0.9992115
## threshold_zoffset[5]    6.788609e-01  1.849909e+00 3060.9606 0.9997678
## threshold_zoffset[6]    1.826523e-01  1.309883e+00 1922.1615 1.0013407
## threshold_zoffset[7]    8.839182e-01  2.106645e+00 3069.5424 0.9995265
## threshold_zoffset[8]    5.106507e-01  1.718732e+00 2721.8085 1.0005418
## threshold_zoffset[9]    8.781003e-02  1.321168e+00 1442.2717 0.9995855
## threshold_zoffset[10]   6.520794e-01  1.904849e+00 3144.6535 0.9991866
## threshold_zoffset[11]   6.118175e-01  1.850301e+00 2824.3703 0.9998624
## threshold_zoffset[12]   6.251963e-01  1.734154e+00 3260.9769 0.9991292
## threshold_zoffset[13]   5.676083e-01  1.708528e+00 3362.0205 0.9998581
## threshold_zoffset[14]   5.850041e-01  1.769982e+00 3235.0569 0.9997765
## threshold_zoffset[15]   1.067931e+00  2.237031e+00 3099.2095 0.9992985
## threshold_zoffset[16]   3.511976e-01  1.573815e+00 2782.6729 0.9995221
## threshold_zoffset[17]   3.852863e-01  1.499374e+00 2897.0324 0.9998643
## threshold_zoffset[18]   6.505960e-02  1.362431e+00 1703.8860 0.9994909
## threshold_zoffset[19]   6.658562e-01  2.027950e+00 3266.8859 0.9995443
## threshold_zoffset[20]   6.147608e-01  1.932124e+00 3613.1074 0.9991100
## threshold_zoffset[21]   7.624301e-01  1.971244e+00 2818.3652 0.9994477
## threshold_zoffset[22]   4.080978e-01  1.586506e+00 2864.1208 0.9990853
## threshold_zoffset[23]   9.409391e-01  2.183757e+00 1977.1129 1.0003816
## threshold_zoffset[24]   6.610699e-01  1.889601e+00 3413.1620 0.9998345
## threshold_zoffset[25]   1.157479e+00  2.424758e+00 2131.5339 1.0007100
## threshold_zoffset[26]   8.265319e-01  2.089616e+00 2728.9775 1.0002104
## threshold_zoffset[27]   7.599540e-01  1.884961e+00 3767.2413 0.9994231
## threshold_zoffset[28]   8.953148e-01  2.171252e+00 2433.0722 1.0014440
## threshold_zoffset[29]   1.266103e+00  2.387224e+00 1658.1068 0.9998111
## threshold_zoffset[30]   9.826926e-01  2.223573e+00 2781.7547 0.9992372
## threshold_zoffset[31]   4.290239e-01  1.592607e+00 2478.4117 0.9997631
## threshold_zoffset[32]   8.407523e-01  2.185344e+00 2652.3018 0.9997316
## threshold_zoffset[33]   2.580964e-01  1.513537e+00 2302.6811 0.9991046
## threshold_zoffset[34]   5.525402e-01  1.763524e+00 2819.5143 0.9990862
## threshold_zoffset[35]   7.347893e-01  1.929713e+00 2345.0178 1.0007581
## threshold_zoffset[36]   2.322596e-01  1.379853e+00 2256.6154 0.9992642
## threshold_zoffset[37]   7.579462e-01  2.141801e+00 2457.4304 0.9997252
## threshold_zoffset[38]   8.446260e-01  1.975197e+00 2962.0889 0.9993558
## threshold_zoffset[39]   1.958739e-01  1.444463e+00 2378.1773 0.9999577
## threshold_zoffset[40]   2.713628e-02  1.219611e+00 1839.2496 0.9993968
## threshold_zoffset[41]   6.305700e-01  1.839063e+00 2350.8899 0.9994067
## threshold_zoffset[42]   8.023876e-01  2.055290e+00 3208.0801 0.9991124
## threshold_zoffset[43]   8.752704e-01  1.960970e+00 2853.9799 1.0004535
## threshold_zoffset[44]   3.008784e-01  1.390744e+00 2896.5080 0.9998649
## threshold_zoffset[45]   5.318673e-01  1.850796e+00 3019.7239 1.0004762
## threshold_zoffset[46]   5.989937e-01  1.997259e+00 3410.1618 0.9997614
## threshold_zoffset[47]   5.632716e-02  1.279481e+00 1634.8974 0.9994490
## threshold_zoffset[48]   4.188516e-02  1.255703e+00 2184.8541 0.9992926
## threshold_zoffset[49]  -6.321500e-03  1.138273e+00 1930.1944 0.9998255
## threshold_zoffset[50]   8.356462e-01  2.294378e+00 2802.0113 0.9990671
## threshold_zoffset[51]   6.611330e-01  1.900850e+00 2537.5654 0.9992715
## threshold_zoffset[52]   9.493552e-01  2.215294e+00 2985.0644 0.9994169
## threshold_zoffset[53]   1.737455e-01  1.365791e+00 1417.0228 1.0008349
## threshold_zoffset[54]   8.945019e-01  2.052905e+00 2952.4252 0.9994623
## threshold_zoffset[55]   9.334255e-01  2.072795e+00 1770.7843 1.0007603
## threshold_zoffset[56]   2.497349e-01  1.524681e+00 2105.9999 0.9993256
## threshold_zoffset[57]   1.474414e-01  1.274075e+00 2293.6307 0.9995354
## threshold_zoffset[58]   8.424080e-01  1.928461e+00 2583.6675 0.9996014
## threshold_zoffset[59]   1.214608e+00  2.436311e+00 1788.7264 0.9999406
## threshold_zoffset[60]   9.874460e-01  2.174301e+00 3205.6612 0.9997935
## threshold_zoffset[61]   1.068573e+00  2.308099e+00 2495.6447 0.9992080
## threshold_zoffset[62]   5.798317e-01  1.726259e+00 3011.4212 0.9996787
## threshold_zoffset[63]   8.585555e-01  2.080160e+00 3079.0233 1.0008273
## threshold_zoffset[64]   1.016425e+00  2.191258e+00 2310.9618 1.0002090
## threshold_zoffset[65]   3.567078e-01  1.510185e+00 2854.2846 1.0003828
## threshold_zoffset[66]   1.225343e+00  2.467917e+00 2109.1983 0.9997095
## threshold_zoffset[67]   1.383168e-01  1.422636e+00 1922.3728 0.9996802
## threshold_zoffset[68]   9.546742e-01  2.121475e+00 2391.6629 0.9991073
## threshold_zoffset[69]   1.927065e-01  1.347533e+00 2106.2988 1.0004749
## threshold_zoffset[70]   4.677645e-02  1.300499e+00 1887.5544 1.0004563
## threshold_zoffset[71]   6.879392e-01  1.807339e+00 3156.1960 1.0003869
## threshold_zoffset[72]   9.328221e-01  2.138740e+00 2384.0318 0.9997127
## threshold_zoffset[73]   7.366234e-01  1.958613e+00 2783.5872 0.9998281
## threshold_zoffset[74]   4.730170e-01  1.571482e+00 3624.2677 0.9993394
## threshold_zoffset[75]   8.126329e-01  1.990167e+00 2743.6761 0.9991223
## threshold_zoffset[76]   5.653806e-01  1.813849e+00 2792.9078 0.9992222
## threshold_zoffset[77]  -3.121742e-01  9.031790e-01 1454.0674 0.9993194
## threshold_zoffset[78]   7.401000e-01  1.884773e+00 3187.8657 0.9992323
## threshold_zoffset[79]   1.013214e-01  1.239305e+00 1531.1571 1.0008150
## threshold_zoffset[80]   9.487678e-01  2.107488e+00 2788.0834 0.9999682
## threshold_zoffset[81]   3.417901e-01  1.485068e+00 2899.4715 1.0003772
## threshold_zoffset[82]   9.941310e-01  2.048171e+00 2501.6232 0.9995496
## threshold_zoffset[83]   8.280174e-01  2.043645e+00 2889.4474 0.9996008
## threshold_zoffset[84]   4.429583e-01  1.648008e+00 2450.3935 1.0006402
## threshold_zoffset[85]   1.447400e-01  1.291854e+00 1900.7533 0.9994639
## threshold_zoffset[86]   6.921997e-01  1.795847e+00 3243.3856 1.0005691
## threshold_zoffset[87]   8.381546e-01  2.042604e+00 3496.1128 0.9993998
## threshold_zoffset[88]   8.073126e-01  1.908636e+00 2974.8819 0.9998263
## threshold_zoffset[89]   9.144240e-01  2.095628e+00 2434.9096 0.9995619
## threshold_zoffset[90]   1.191398e+00  2.419951e+00 1648.6034 0.9998045
## threshold_zoffset[91]   9.509401e-02  1.254443e+00 1928.9170 0.9992299
## threshold_zoffset[92]   9.910589e-01  2.170041e+00 2871.9520 0.9990750
## threshold_zoffset[93]   6.956384e-01  1.898906e+00 2929.2352 0.9991694
## threshold_zoffset[94]   6.866961e-01  1.940090e+00 3412.6148 0.9994882
## threshold_zoffset[95]   6.932328e-01  1.918065e+00 2437.0496 1.0020599
## threshold_zoffset[96]   5.313559e-01  1.772253e+00 2504.9994 0.9999300
## threshold_zoffset[97]   5.125748e-01  1.810696e+00 2916.4558 0.9992021
## threshold_zoffset[98]   8.632054e-02  1.426833e+00 2070.2915 0.9991183
## threshold_zoffset[99]   8.835271e-01  2.035701e+00 3017.7058 0.9995208
## threshold_zoffset[100]  7.484293e-01  1.959980e+00 2708.2529 0.9998273
## threshold_zoffset[101]  7.360177e-01  1.986838e+00 3608.0298 0.9997411
## threshold_zoffset[102]  3.718339e-01  1.609327e+00 2472.4021 0.9992539
## threshold_zoffset[103]  7.302483e-01  1.943264e+00 3790.7601 0.9993023
## threshold_zoffset[104]  3.719914e-01  1.580763e+00 2013.0413 0.9996976
## threshold_zoffset[105]  5.092498e-01  1.730912e+00 2602.9341 0.9998100
## threshold_zoffset[106]  8.488072e-01  1.967294e+00 3254.2634 0.9994914
## threshold_zoffset[107]  2.031903e+00  3.494835e+00  614.1251 1.0009639
## threshold_zoffset[108]  5.421769e-01  1.723639e+00 3263.2322 0.9993440
## threshold_zoffset[109]  5.339654e-01  1.695183e+00 3387.3577 0.9990986
## threshold_zoffset[110]  8.553040e-01  2.135391e+00 2774.8595 1.0012833
## threshold_zoffset[111]  7.752137e-01  1.907900e+00 2387.9006 0.9993525
## threshold_zoffset[112]  7.339097e-01  1.903338e+00 3342.2415 0.9998131
## threshold_zoffset[113]  2.918663e-01  1.572098e+00 1928.8935 1.0008544
## threshold_zoffset[114]  5.527817e-01  1.818538e+00 2926.5215 0.9990374
## threshold_zoffset[115]  3.358443e-01  1.531514e+00 2920.6885 0.9992996
## threshold_zoffset[116]  6.194060e-01  1.761931e+00 3175.8235 0.9996047
## threshold_zoffset[117]  9.242925e-01  2.071268e+00 2467.9753 0.9991157
## threshold_zoffset[118]  7.032529e-01  2.012599e+00 2885.6507 0.9999957
## threshold_zoffset[119]  1.009879e+00  2.165961e+00 3041.8518 1.0001325
## threshold_zoffset[120]  5.702089e-01  1.804668e+00 2812.8309 0.9997857
## threshold_zoffset[121]  6.847273e-01  1.804729e+00 2540.0953 0.9994718
## threshold_zoffset[122]  5.308664e-01  1.718316e+00 3089.2488 0.9992266
## threshold_zoffset[123]  6.052157e-01  1.784208e+00 2909.2289 0.9993812
## threshold_zoffset[124]  1.011104e+00  2.095646e+00 2031.1374 0.9995932
## threshold_zoffset[125]  9.779850e-01  2.092523e+00 2077.9971 0.9990207
## threshold_zoffset[126]  9.136764e-01  2.159931e+00 3175.2200 0.9993203
## threshold_zoffset[127]  1.083626e+00  2.198528e+00 2160.2017 0.9994405
## threshold_zoffset[128]  5.611058e-01  1.800986e+00 3444.5220 0.9995426
## threshold_zoffset[129]  9.152149e-02  1.278252e+00 1851.6647 0.9998279
## threshold_zoffset[130]  9.177992e-01  2.097092e+00 2357.8840 0.9993777
## threshold_zoffset[131]  5.386109e-01  1.772672e+00 2430.2029 0.9992460
## threshold_zoffset[132]  8.805041e-01  2.155577e+00 3134.3584 0.9994180
## threshold_zoffset[133]  5.263233e-01  1.660168e+00 2950.9987 0.9990816
## threshold_zoffset[134]  9.659014e-01  2.220549e+00 2851.0725 1.0009141
## threshold_zoffset[135]  6.610659e-01  1.847567e+00 3604.3796 0.9992346
## threshold_zoffset[136]  9.670864e-01  2.213453e+00 2753.9190 0.9993653
## threshold_zoffset[137]  4.565306e-01  1.559765e+00 2746.5531 0.9999311
## threshold_zoffset[138]  8.581589e-01  1.977518e+00 2350.2275 0.9996607
## threshold_zoffset[139]  1.149502e+00  2.374797e+00 1743.9421 0.9999617
## threshold_zoffset[140]  5.210776e-01  1.758600e+00 2683.1810 0.9994212
## threshold_zoffset[141]  6.753827e-01  1.799934e+00 2668.4347 0.9994869
## threshold_zoffset[142]  8.747615e-01  1.980942e+00 2828.4029 0.9997059
## threshold_zoffset[143]  7.742023e-01  1.877388e+00 2415.3341 1.0001368
## threshold_zoffset[144]  7.957519e-01  1.992079e+00 2889.9381 0.9991754
## threshold_zoffset[145]  6.624290e-01  1.851852e+00 2586.6321 0.9993311
## threshold_zoffset[146]  9.189094e-01  2.154578e+00 2879.7293 1.0005553
## threshold_zoffset[147] -3.534751e-01  8.856257e-01  905.6538 1.0001379
## threshold_zoffset[148]  6.564037e-01  1.879797e+00 2860.4935 0.9997985
## threshold_zoffset[149]  2.065367e-01  1.355459e+00 2519.0055 0.9993398
## threshold_zoffset[150]  4.792134e-01  1.777841e+00 3262.6212 1.0003322
## spread_zoffset[1]       1.114136e+00  2.470703e+00 1658.6092 0.9994392
## spread_zoffset[2]       1.026611e+00  2.025149e+00 2165.9888 1.0004830
## spread_zoffset[3]       7.190184e-01  1.790635e+00 2952.1945 0.9992864
## spread_zoffset[4]       1.115291e+00  2.126896e+00 2307.5597 1.0009022
## spread_zoffset[5]       1.023468e+00  2.089152e+00 2188.9356 0.9999635
## spread_zoffset[6]      -2.241830e-01  9.853665e-01 2563.6326 1.0005738
## spread_zoffset[7]       1.032512e+00  1.994768e+00 2259.2649 1.0007608
## spread_zoffset[8]       1.187942e+00  2.371340e+00 1421.4443 1.0033486
## spread_zoffset[9]      -2.915033e-01  7.735787e-01 2874.2868 1.0023630
## spread_zoffset[10]      1.436665e+00  2.531136e+00 1222.4579 1.0014558
## spread_zoffset[11]      5.758569e-01  1.650836e+00 2495.3515 0.9993814
## spread_zoffset[12]      7.800700e-02  1.027627e+00 2672.1045 0.9992846
## spread_zoffset[13]      6.343726e-02  1.116861e+00 3073.6249 1.0000863
## spread_zoffset[14]      6.347723e-01  1.977697e+00 2933.4231 0.9995305
## spread_zoffset[15]      1.242665e+00  2.329062e+00 1884.9869 1.0018507
## spread_zoffset[16]     -2.161378e-01  8.204771e-01 2857.8513 1.0000343
## spread_zoffset[17]      6.778347e-01  1.616943e+00 3014.0077 0.9993973
## spread_zoffset[18]      5.287162e-02  1.022211e+00 2317.8507 1.0001383
## spread_zoffset[19]      6.898855e-01  2.015756e+00 2670.2916 0.9993549
## spread_zoffset[20]      5.091983e-01  1.524902e+00 2773.8336 1.0000479
## spread_zoffset[21]      9.345827e-01  1.919444e+00 2292.4364 0.9995541
## spread_zoffset[22]      2.402498e-01  1.178710e+00 2455.7393 1.0000716
## spread_zoffset[23]      8.237384e-01  1.766791e+00 2407.1487 0.9991471
## spread_zoffset[24]      7.246442e-01  1.980662e+00 3323.4073 0.9997488
## spread_zoffset[25]      1.348081e+00  2.348533e+00 2301.3319 1.0007078
## spread_zoffset[26]      9.632822e-01  2.177498e+00 2011.7692 0.9993946
## spread_zoffset[27]      2.906631e-01  1.221850e+00 2583.1955 1.0009871
## spread_zoffset[28]      1.109172e+00  2.093541e+00 2556.0670 1.0001282
## spread_zoffset[29]      7.059487e-01  1.720952e+00 2023.3508 1.0009498
## spread_zoffset[30]      1.021643e+00  2.397751e+00  935.7410 1.0032493
## spread_zoffset[31]      3.564018e-02  1.105912e+00 2508.9393 0.9992169
## spread_zoffset[32]      1.040601e+00  2.542697e+00 1477.4744 1.0030785
## spread_zoffset[33]      8.913627e-01  1.850999e+00 2885.6971 0.9996004
## spread_zoffset[34]      6.060018e-01  1.698593e+00 2858.6485 0.9994846
## spread_zoffset[35]      4.248652e-01  1.595955e+00 3485.9958 0.9992002
## spread_zoffset[36]      4.241636e-01  1.448335e+00 2533.1014 0.9994193
## spread_zoffset[37]      1.116910e+00  2.506001e+00 2316.9223 0.9996973
## spread_zoffset[38]      7.013539e-01  1.774022e+00 2986.9126 0.9992665
## spread_zoffset[39]      6.954588e-01  1.730235e+00 2678.3174 0.9995715
## spread_zoffset[40]     -2.002543e-01  8.974843e-01 2513.7882 1.0003000
## spread_zoffset[41]      5.752379e-01  1.668837e+00 2098.8410 1.0006321
## spread_zoffset[42]      9.122910e-01  2.191964e+00 1928.3584 0.9991111
## spread_zoffset[43]      1.138675e+00  2.291364e+00 1878.1851 0.9990337
## spread_zoffset[44]      3.745928e-01  1.428232e+00 3520.4613 1.0002863
## spread_zoffset[45]      1.460780e-01  1.127900e+00 2499.6022 1.0006455
## spread_zoffset[46]      6.686993e-01  1.970815e+00 2623.8621 0.9998536
## spread_zoffset[47]     -6.454667e-01  5.103917e-01 2557.5918 1.0005931
## spread_zoffset[48]      2.019298e-01  1.363741e+00 2668.3997 1.0000987
## spread_zoffset[49]     -7.060799e-02  9.728548e-01 2857.2202 0.9993322
## spread_zoffset[50]      1.073109e+00  2.388811e+00 3144.7262 0.9999044
## spread_zoffset[51]      1.112006e+00  2.090096e+00 1813.7490 1.0025506
## spread_zoffset[52]      1.211318e+00  2.215102e+00 2558.4310 0.9996607
## spread_zoffset[53]     -1.432052e-01  9.515523e-01 2710.7752 0.9994025
## spread_zoffset[54]      3.249655e-01  1.312628e+00 2712.6841 1.0000357
## spread_zoffset[55]      5.203669e-01  1.422777e+00 2648.7406 0.9991303
## spread_zoffset[56]     -2.815611e-01  8.674216e-01 2748.5718 0.9998290
## spread_zoffset[57]     -1.365181e-01  9.192480e-01 3590.7643 0.9992716
## spread_zoffset[58]     -1.079079e-01  8.784919e-01 2437.4342 0.9990972
## spread_zoffset[59]      1.014755e+00  1.930286e+00 2442.8354 0.9998867
## spread_zoffset[60]      1.020496e+00  2.130654e+00 2250.1607 0.9992642
## spread_zoffset[61]      7.480996e-01  1.779498e+00 2202.9978 1.0004953
## spread_zoffset[62]      2.423026e-01  1.351732e+00 2806.0035 0.9996130
## spread_zoffset[63]      1.071896e+00  2.175267e+00 2154.2326 0.9991941
## spread_zoffset[64]      1.176078e+00  2.246143e+00 1929.8006 1.0001791
## spread_zoffset[65]      1.071032e+00  2.006777e+00 3339.0688 0.9991163
## spread_zoffset[66]      8.620126e-01  1.822451e+00 2099.5908 0.9993227
## spread_zoffset[67]     -9.058036e-02  9.598221e-01 3130.3630 0.9999847
## spread_zoffset[68]      7.792353e-01  2.056222e+00 1698.7587 0.9990765
## spread_zoffset[69]     -8.414153e-01  2.633972e-01 2345.6247 1.0006934
## spread_zoffset[70]      5.604803e-01  1.633344e+00 2583.2494 1.0006679
## spread_zoffset[71]      1.127153e+00  2.128016e+00 2053.5794 1.0001383
## spread_zoffset[72]      1.018549e+00  2.262532e+00 2754.8120 1.0001736
## spread_zoffset[73]      6.701682e-01  1.701861e+00 2691.3719 1.0012602
## spread_zoffset[74]      5.159575e-01  1.653515e+00 2352.7436 0.9991466
## spread_zoffset[75]      7.642571e-01  1.692142e+00 3617.9773 0.9998072
## spread_zoffset[76]      7.028671e-01  1.750380e+00 2007.4109 0.9998906
## spread_zoffset[77]     -1.156668e+00  8.883901e-02 1402.9022 0.9996497
## spread_zoffset[78]      1.603733e-01  1.122199e+00 2984.5839 0.9993655
## spread_zoffset[79]      7.890104e-01  1.782527e+00 3080.1049 1.0000266
## spread_zoffset[80]      8.710632e-01  2.004664e+00 1986.9088 0.9998718
## spread_zoffset[81]      7.163346e-01  1.786643e+00 2740.5189 0.9993748
## spread_zoffset[82]      1.022213e+00  2.006301e+00 1989.4206 0.9999831
## spread_zoffset[83]      3.665807e-01  1.408536e+00 2668.2957 1.0005994
## spread_zoffset[84]     -3.755554e-01  7.400263e-01 2765.6068 1.0010597
## spread_zoffset[85]     -4.830105e-01  7.413392e-01 2707.0427 0.9996513
## spread_zoffset[86]      3.333089e-01  1.773037e+00 1198.3819 0.9994163
## spread_zoffset[87]      1.013408e+00  2.403024e+00 1529.0642 1.0007487
## spread_zoffset[88]      8.705365e-01  1.756781e+00 2296.3461 0.9990583
## spread_zoffset[89]      1.011997e+00  2.168518e+00 1821.8179 0.9991993
## spread_zoffset[90]      1.504031e+00  2.444528e+00 2107.6137 1.0013144
## spread_zoffset[91]     -1.415224e-01  9.593565e-01 3518.3124 0.9994122
## spread_zoffset[92]      8.349391e-01  1.773016e+00 2280.3782 0.9995795
## spread_zoffset[93]      1.109759e+00  2.304410e+00 1175.2522 0.9993429
## spread_zoffset[94]      7.386968e-01  2.182122e+00 2236.4540 0.9992450
## spread_zoffset[95]      7.392469e-01  1.722650e+00 2479.9454 1.0011148
## spread_zoffset[96]      8.189840e-01  2.312723e+00  929.2061 1.0031711
## spread_zoffset[97]      8.584651e-01  2.192129e+00 3292.4833 0.9992616
## spread_zoffset[98]     -4.255525e-01  7.141994e-01 1888.8343 0.9996569
## spread_zoffset[99]      1.142748e+00  2.107249e+00 2161.3565 1.0000444
## spread_zoffset[100]     8.311094e-01  1.784956e+00 2529.1230 0.9990974
## spread_zoffset[101]     1.626999e+00  2.690446e+00 1658.3217 1.0005463
## spread_zoffset[102]     2.045089e-01  1.283325e+00 3041.3424 0.9999522
## spread_zoffset[103]     8.458207e-01  2.113733e+00 2890.4905 1.0020159
## spread_zoffset[104]     3.283740e-01  1.408447e+00 2775.2855 0.9998029
## spread_zoffset[105]     5.798870e-01  1.518721e+00 2153.0881 0.9997339
## spread_zoffset[106]     1.111268e+00  2.159019e+00 2342.7853 1.0006525
## spread_zoffset[107]     1.371625e+00  2.290355e+00  915.2226 1.0020697
## spread_zoffset[108]     5.390567e-01  1.603707e+00 2068.3543 0.9996243
## spread_zoffset[109]     4.590977e-01  1.509339e+00 3232.9981 0.9992978
## spread_zoffset[110]     1.137006e+00  2.600129e+00 1144.5069 1.0006029
## spread_zoffset[111]     2.478669e-01  1.285535e+00 2148.6901 1.0009146
## spread_zoffset[112]     2.576310e-01  1.329652e+00 2524.7499 1.0001099
## spread_zoffset[113]     8.668616e-02  1.122917e+00 2449.6347 0.9995095
## spread_zoffset[114]     9.980776e-01  2.433127e+00 1253.2130 0.9996806
## spread_zoffset[115]     4.691001e-01  1.466976e+00 2775.7087 0.9999784
## spread_zoffset[116]     2.795596e-01  1.344578e+00 2888.5219 0.9993775
## spread_zoffset[117]     8.697395e-01  1.908526e+00 2004.8969 1.0022765
## spread_zoffset[118]     9.141609e-01  2.272699e+00 2023.5587 1.0016608
## spread_zoffset[119]     1.550248e-01  1.128324e+00 2671.1056 1.0000440
## spread_zoffset[120]     1.105373e+00  2.106262e+00 2595.3390 1.0006448
## spread_zoffset[121]     1.771298e-01  1.237057e+00 2277.0739 1.0022826
## spread_zoffset[122]    -2.961315e-01  7.185324e-01 3622.9595 1.0010511
## spread_zoffset[123]     2.411478e-01  1.247183e+00 3285.0275 0.9997545
## spread_zoffset[124]     7.969502e-01  1.788659e+00 2716.9999 0.9996458
## spread_zoffset[125]     4.982325e-01  1.450850e+00 2598.8383 1.0000500
## spread_zoffset[126]     9.594637e-01  2.169645e+00 1562.2305 1.0031568
## spread_zoffset[127]     1.165990e+00  2.154768e+00 2279.7765 0.9997958
## spread_zoffset[128]     4.336237e-01  1.849053e+00 1936.7195 1.0010635
## spread_zoffset[129]    -1.526304e-01  9.044958e-01 3578.5235 0.9997757
## spread_zoffset[130]     1.109133e+00  2.014717e+00 2200.6213 1.0017181
## spread_zoffset[131]    -8.926846e-02  1.013611e+00 3004.9301 0.9998534
## spread_zoffset[132]     1.039342e+00  2.367621e+00 1504.4160 1.0027227
## spread_zoffset[133]     1.217367e-01  1.217718e+00 2889.4412 0.9991322
## spread_zoffset[134]     7.879783e-01  1.736017e+00 2480.2878 0.9995939
## spread_zoffset[135]     5.973203e-01  1.876191e+00 2706.8766 1.0013398
## spread_zoffset[136]     1.316114e+00  2.261755e+00 2260.7847 0.9991965
## spread_zoffset[137]     1.249167e-01  1.193600e+00 3328.7853 1.0004375
## spread_zoffset[138]     3.519852e-01  1.345732e+00 2445.3518 0.9991008
## spread_zoffset[139]     8.177858e-01  1.769807e+00 1961.2961 0.9993942
## spread_zoffset[140]    -3.293726e-02  9.423916e-01 3299.5709 0.9995984
## spread_zoffset[141]     1.004828e+00  2.072470e+00 2026.4586 1.0006808
## spread_zoffset[142]     5.697750e-01  1.808748e+00 1712.5052 1.0001219
## spread_zoffset[143]     1.664911e-01  1.221764e+00 3135.3471 0.9992520
## spread_zoffset[144]     6.923115e-01  1.658538e+00 2877.7835 1.0001119
## spread_zoffset[145]     1.047159e+00  2.202816e+00 1613.0784 1.0022256
## spread_zoffset[146]     8.004416e-01  2.031926e+00 1734.6049 0.9995829
## spread_zoffset[147]    -8.151182e-01  3.476192e-01 3094.4203 1.0002972
## spread_zoffset[148]     9.627325e-01  2.142944e+00 1755.4826 1.0002961
## spread_zoffset[149]     6.312041e-02  1.036097e+00 2317.7654 1.0003871
## spread_zoffset[150]     7.612884e-02  1.076198e+00 2144.8329 0.9996068
## lapse_zoffset[1]        1.421472e+00  1.775474e+00  684.2549 1.0005507
## lapse_zoffset[2]        5.317742e-01  1.159945e+00 1568.1569 1.0024368
## lapse_zoffset[3]        5.981355e-01  1.157852e+00 1208.8798 1.0005537
## lapse_zoffset[4]        1.480562e-01  8.462105e-01 2234.6016 0.9991737
## lapse_zoffset[5]        6.247460e-01  1.086450e+00  969.0641 1.0029882
## lapse_zoffset[6]       -1.705963e-02  6.980221e-01 2248.8229 0.9994333
## lapse_zoffset[7]        4.290510e-01  1.072211e+00 1553.5028 0.9992732
## lapse_zoffset[8]        8.562402e-01  1.261728e+00  576.3512 1.0045919
## lapse_zoffset[9]       -1.008097e-01  5.937019e-01 2499.3781 0.9992963
## lapse_zoffset[10]       1.104287e+00  1.523275e+00  495.2027 1.0002021
## lapse_zoffset[11]       7.076932e-01  1.222407e+00 1246.0168 1.0005045
## lapse_zoffset[12]      -8.338514e-02  5.761569e-01 1921.3206 0.9995549
## lapse_zoffset[13]      -1.081394e-01  6.011061e-01 2110.5864 1.0011566
## lapse_zoffset[14]       1.567387e+00  1.880376e+00  677.0232 1.0036453
## lapse_zoffset[15]       8.789867e-01  1.426560e+00  768.9989 1.0034976
## lapse_zoffset[16]      -1.945724e-01  5.243316e-01 2460.3161 0.9998540
## lapse_zoffset[17]       3.081010e-01  9.497304e-01 1882.3635 1.0009230
## lapse_zoffset[18]      -8.096710e-02  6.424212e-01 1957.7664 0.9997073
## lapse_zoffset[19]       2.118206e+00  2.470206e+00  411.2709 1.0076437
## lapse_zoffset[20]       4.585539e-02  7.506412e-01 2579.6998 1.0010309
## lapse_zoffset[21]       1.596057e-01  8.376260e-01 1894.4471 0.9991852
## lapse_zoffset[22]      -1.637946e-01  5.124828e-01 2191.5439 1.0004285
## lapse_zoffset[23]       4.072536e-01  1.081879e+00 1600.8439 0.9997031
## lapse_zoffset[24]       2.284180e+00  2.652908e+00  412.0609 1.0079929
## lapse_zoffset[25]       8.655882e-01  1.354994e+00  983.0603 1.0013934
## lapse_zoffset[26]       8.329428e-01  1.271672e+00  635.1815 1.0006291
## lapse_zoffset[27]      -4.154842e-02  6.376057e-01 1950.6944 0.9990922
## lapse_zoffset[28]       4.713209e-01  1.071050e+00 1699.5130 1.0005544
## lapse_zoffset[29]       1.241700e-01  8.960301e-01 2417.6926 0.9995847
## lapse_zoffset[30]       1.213174e+00  1.556315e+00  409.8776 1.0010184
## lapse_zoffset[31]      -2.737444e-03  7.187485e-01 1727.8418 0.9995764
## lapse_zoffset[32]       1.432525e+00  1.774135e+00  568.6396 1.0040258
## lapse_zoffset[33]       1.062547e-01  8.496684e-01 2320.1865 1.0005523
## lapse_zoffset[34]       1.931256e-01  8.417661e-01 2261.8747 0.9999117
## lapse_zoffset[35]       1.807392e-01  8.292970e-01 2111.0643 1.0006661
## lapse_zoffset[36]       3.298360e-02  8.088811e-01 2424.6490 0.9993417
## lapse_zoffset[37]       1.604583e+00  1.950244e+00  695.2469 1.0027423
## lapse_zoffset[38]       1.920326e-01  9.327281e-01 2192.9083 0.9996211
## lapse_zoffset[39]      -1.014469e-02  6.199391e-01 1770.1429 0.9994507
## lapse_zoffset[40]      -1.658288e-01  5.550920e-01 2053.2750 1.0001285
## lapse_zoffset[41]       5.042671e-01  1.056670e+00 1324.9954 1.0003176
## lapse_zoffset[42]       1.682359e+00  2.012007e+00  613.6296 1.0042936
## lapse_zoffset[43]       1.063634e+00  1.518257e+00  781.4806 1.0000835
## lapse_zoffset[44]       4.394260e-02  8.477977e-01 2641.7659 0.9996260
## lapse_zoffset[45]      -7.347404e-02  6.093258e-01 2144.7822 0.9996038
## lapse_zoffset[46]       2.257185e+00  2.599852e+00  402.3685 1.0070761
## lapse_zoffset[47]      -2.678056e-01  4.395032e-01 1972.5930 0.9993184
## lapse_zoffset[48]      -5.897517e-02  6.665436e-01 2167.0039 0.9999136
## lapse_zoffset[49]      -1.088589e-01  6.076646e-01 2050.4796 0.9994243
## lapse_zoffset[50]       1.672614e+00  2.004229e+00  660.3831 1.0067786
## lapse_zoffset[51]       3.523191e-01  9.361491e-01 1701.4667 1.0019132
## lapse_zoffset[52]       4.732450e-01  1.113740e+00 1677.0846 1.0023577
## lapse_zoffset[53]      -6.166601e-02  5.822504e-01 2292.7636 0.9996681
## lapse_zoffset[54]       5.964714e-02  7.181439e-01 2164.8289 1.0004348
## lapse_zoffset[55]       4.216777e-02  7.702490e-01 2082.4630 1.0005592
## lapse_zoffset[56]      -1.571474e-01  5.379213e-01 2183.9691 0.9994895
## lapse_zoffset[57]      -1.993806e-01  5.162739e-01 2020.1075 0.9994241
## lapse_zoffset[58]      -7.123120e-02  6.099523e-01 2097.0398 0.9991852
## lapse_zoffset[59]       2.193574e-01  8.861268e-01 1863.6289 1.0000572
## lapse_zoffset[60]       7.010614e-01  1.183536e+00 1177.8179 1.0014027
## lapse_zoffset[61]       6.283547e-02  7.993360e-01 1985.5918 0.9991831
## lapse_zoffset[62]       3.932908e-01  9.157418e-01 1442.5643 1.0006745
## lapse_zoffset[63]       4.312698e-01  9.718841e-01 1658.3570 0.9993801
## lapse_zoffset[64]       5.825570e-01  1.120801e+00  962.6186 1.0059567
## lapse_zoffset[65]       4.329887e-02  7.966173e-01 2190.6497 1.0006540
## lapse_zoffset[66]       3.953804e-01  9.336904e-01 1672.8117 0.9997241
## lapse_zoffset[67]      -1.370704e-01  6.110865e-01 2929.7340 0.9994451
## lapse_zoffset[68]       1.038880e+00  1.430820e+00  676.7804 1.0005618
## lapse_zoffset[69]      -1.418178e-01  5.395402e-01 2477.6054 0.9995280
## lapse_zoffset[70]       1.104060e-01  8.186416e-01 1913.6689 1.0000182
## lapse_zoffset[71]       6.543399e-01  1.174292e+00 1152.3497 1.0001473
## lapse_zoffset[72]       1.892142e+00  2.246093e+00  678.3628 1.0016416
## lapse_zoffset[73]       4.327342e-01  9.766765e-01 1454.5010 1.0010594
## lapse_zoffset[74]      -5.374530e-03  7.398748e-01 2213.6880 0.9994574
## lapse_zoffset[75]       8.919433e-02  7.829922e-01 2505.4777 0.9993197
## lapse_zoffset[76]       7.242675e-01  1.253020e+00 1084.8198 0.9993344
## lapse_zoffset[77]      -1.930499e-01  4.884018e-01 3135.5367 0.9991663
## lapse_zoffset[78]      -1.021661e-02  7.204415e-01 2522.7420 0.9991216
## lapse_zoffset[79]       1.420595e-01  7.846235e-01 2109.8679 1.0008221
## lapse_zoffset[80]       6.658546e-01  1.125978e+00 1115.1113 0.9995261
## lapse_zoffset[81]       3.364649e-01  9.078212e-01 1612.9761 0.9997796
## lapse_zoffset[82]       3.884419e-01  1.005629e+00 1911.2279 1.0002907
## lapse_zoffset[83]      -3.781703e-02  6.920551e-01 2015.8242 1.0003550
## lapse_zoffset[84]      -9.394898e-02  6.407343e-01 2664.8681 0.9992940
## lapse_zoffset[85]      -1.281612e-01  5.775111e-01 2415.0341 0.9993971
## lapse_zoffset[86]       1.145972e+00  1.503182e+00  395.9502 1.0017208
## lapse_zoffset[87]       1.327145e+00  1.700953e+00  364.3455 1.0108517
## lapse_zoffset[88]       2.741435e-01  9.165697e-01 2049.7408 0.9990204
## lapse_zoffset[89]       8.741184e-01  1.335721e+00 1081.7201 0.9993161
## lapse_zoffset[90]       7.232504e-01  1.268870e+00 1316.1718 0.9993091
## lapse_zoffset[91]      -3.887691e-02  6.851499e-01 2044.3607 1.0040711
## lapse_zoffset[92]       2.257444e-01  8.292359e-01 2115.0356 0.9998513
## lapse_zoffset[93]       1.094493e+00  1.516049e+00  487.3410 1.0018768
## lapse_zoffset[94]       1.660315e+00  1.996536e+00  646.6387 1.0034283
## lapse_zoffset[95]       1.154981e-01  8.799225e-01 2280.7105 0.9991034
## lapse_zoffset[96]       1.399877e+00  1.732360e+00  443.8367 1.0064341
## lapse_zoffset[97]       2.104798e+00  2.449609e+00  425.6016 1.0097300
## lapse_zoffset[98]      -2.163505e-01  5.039066e-01 2072.6235 0.9995327
## lapse_zoffset[99]       4.637315e-01  1.076194e+00 1718.1066 0.9992042
## lapse_zoffset[100]      1.809206e-01  8.994912e-01 2029.3925 0.9996805
## lapse_zoffset[101]      7.846698e-01  1.245469e+00  960.8016 1.0036116
## lapse_zoffset[102]     -5.315129e-02  6.770861e-01 2284.4557 1.0019993
## lapse_zoffset[103]      1.833805e+00  2.166603e+00  457.3731 1.0085365
## lapse_zoffset[104]      5.304690e-02  7.091019e-01 1844.0056 0.9993826
## lapse_zoffset[105]      1.963606e-01  8.488365e-01 1703.9163 0.9996420
## lapse_zoffset[106]      5.916354e-01  1.110830e+00 1162.4620 1.0007583
## lapse_zoffset[107]      4.671779e-01  1.151785e+00 1398.3116 1.0032555
## lapse_zoffset[108]      4.768589e-03  6.205177e-01 1980.3368 0.9994721
## lapse_zoffset[109]      3.694343e-02  8.010064e-01 2613.3837 0.9996423
## lapse_zoffset[110]      1.348427e+00  1.695995e+00  394.5374 1.0014284
## lapse_zoffset[111]      4.230686e-02  7.770836e-01 2663.0395 0.9994589
## lapse_zoffset[112]     -4.302386e-02  6.544701e-01 1981.6846 0.9999348
## lapse_zoffset[113]     -1.387495e-01  5.728558e-01 2016.4836 0.9998466
## lapse_zoffset[114]      1.367141e+00  1.728895e+00  504.5092 0.9999203
## lapse_zoffset[115]      4.613522e-03  7.263643e-01 2551.8097 1.0002824
## lapse_zoffset[116]      6.244611e-02  8.169071e-01 2024.9061 0.9993681
## lapse_zoffset[117]      7.018194e-01  1.205322e+00 1227.5593 1.0039926
## lapse_zoffset[118]      1.631285e+00  1.963823e+00  711.9800 1.0008306
## lapse_zoffset[119]     -7.303115e-02  6.344547e-01 2044.2267 1.0000987
## lapse_zoffset[120]      1.126993e-01  8.048572e-01 2267.8149 0.9999476
## lapse_zoffset[121]     -1.402376e-01  5.748585e-01 2077.2903 1.0010775
## lapse_zoffset[122]     -3.553801e-02  6.694404e-01 1647.5190 0.9994672
## lapse_zoffset[123]      3.687427e-02  7.750894e-01 1875.5130 0.9990694
## lapse_zoffset[124]      1.513032e-01  8.882159e-01 2267.3822 0.9993620
## lapse_zoffset[125]      6.668821e-02  7.728772e-01 2114.0561 0.9996190
## lapse_zoffset[126]      9.387690e-01  1.424941e+00  747.3518 1.0028875
## lapse_zoffset[127]      7.014011e-01  1.261169e+00 1618.2648 1.0008482
## lapse_zoffset[128]      1.672018e+00  1.986435e+00  612.9470 1.0055424
## lapse_zoffset[129]     -1.076674e-01  6.270909e-01 1853.4806 1.0005517
## lapse_zoffset[130]      4.973842e-01  1.117400e+00 1687.4492 1.0012788
## lapse_zoffset[131]      3.689071e-03  6.839579e-01 2344.1254 0.9993752
## lapse_zoffset[132]      1.003534e+00  1.410348e+00  759.2455 1.0033386
## lapse_zoffset[133]     -8.833832e-02  6.027015e-01 2382.6201 0.9998085
## lapse_zoffset[134]      1.910425e-01  9.267664e-01 1884.7303 1.0003555
## lapse_zoffset[135]      2.015036e+00  2.336336e+00  523.4099 1.0036528
## lapse_zoffset[136]      2.917924e-01  1.039884e+00 2053.8662 0.9991969
## lapse_zoffset[137]      2.476773e-02  7.459669e-01 2369.0932 0.9992186
## lapse_zoffset[138]      8.075929e-02  7.776351e-01 2343.8926 0.9996641
## lapse_zoffset[139]      2.607536e-01  9.674912e-01 1884.2114 0.9990120
## lapse_zoffset[140]     -3.972119e-02  7.142285e-01 2226.9844 0.9999703
## lapse_zoffset[141]      3.499252e-01  9.564331e-01 1723.2024 1.0004403
## lapse_zoffset[142]      9.560164e-01  1.360241e+00  871.6547 1.0003210
## lapse_zoffset[143]     -6.313177e-03  7.530539e-01 2037.6087 1.0000558
## lapse_zoffset[144]      4.064882e-01  9.908585e-01 1614.6439 1.0003700
## lapse_zoffset[145]      9.966665e-01  1.362926e+00  645.2005 1.0074037
## lapse_zoffset[146]      8.769335e-01  1.328813e+00  903.6062 1.0045786
## lapse_zoffset[147]     -2.820644e-01  4.165466e-01 2314.3757 0.9993470
## lapse_zoffset[148]      9.743668e-01  1.441204e+00  805.1782 1.0012537
## lapse_zoffset[149]     -4.774593e-02  6.348197e-01 2448.6478 0.9991497
## lapse_zoffset[150]     -1.566121e-02  7.169786e-01 2406.1911 0.9995141
## threshold[1]            2.775604e+00  3.482801e+00 2561.9089 1.0002414
## threshold[2]            2.598185e+00  3.152893e+00 2667.3120 0.9994045
## threshold[3]            2.515013e+00  2.939852e+00 4338.4264 0.9994375
## threshold[4]            2.547429e+00  3.036408e+00 2738.9769 0.9997944
## threshold[5]            2.538238e+00  3.083864e+00 3127.5822 1.0000699
## threshold[6]            2.430017e+00  2.716663e+00 1865.7225 1.0007425
## threshold[7]            2.647744e+00  3.202064e+00 2462.8976 0.9995982
## threshold[8]            2.488647e+00  2.977588e+00 3211.1082 1.0008251
## threshold[9]            2.594966e+00  2.904110e+00 1488.7373 0.9998514
## threshold[10]           2.557153e+00  3.062996e+00 2919.8769 0.9997186
## threshold[11]           2.547033e+00  2.959555e+00 2970.0378 0.9996848
## threshold[12]           2.531754e+00  2.970965e+00 3072.9768 0.9991383
## threshold[13]           2.711637e+00  3.166716e+00 3383.7406 0.9994205
## threshold[14]           2.513366e+00  3.041521e+00 2936.3507 0.9993424
## threshold[15]           2.675533e+00  3.277551e+00 1938.5239 0.9991812
## threshold[16]           2.447167e+00  2.835451e+00 3179.5314 0.9994679
## threshold[17]           2.483340e+00  2.852992e+00 2845.8201 0.9993783
## threshold[18]           2.579869e+00  2.925124e+00 1519.2709 0.9999730
## threshold[19]           2.760906e+00  3.352842e+00 2866.5726 0.9994844
## threshold[20]           2.715200e+00  3.184777e+00 3184.6410 0.9994357
## threshold[21]           2.593059e+00  3.121864e+00 2135.9822 0.9995707
## threshold[22]           2.472141e+00  2.833652e+00 3305.3234 0.9993470
## threshold[23]           2.655703e+00  3.231340e+00 1455.0914 1.0016632
## threshold[24]           2.745348e+00  3.361116e+00 2642.4535 1.0001582
## threshold[25]           2.928737e+00  3.717690e+00  933.8654 1.0024732
## threshold[26]           2.610066e+00  3.181789e+00 2047.8134 0.9998710
## threshold[27]           2.782596e+00  3.301837e+00 2749.6963 0.9997059
## threshold[28]           2.843334e+00  3.480280e+00 1828.0196 1.0028878
## threshold[29]           2.999877e+00  3.645340e+00  816.3379 1.0015789
## threshold[30]           2.651721e+00  3.256472e+00 1385.0379 0.9997034
## threshold[31]           2.480746e+00  2.859445e+00 3196.2492 0.9991776
## threshold[32]           2.820334e+00  3.475840e+00 2029.9721 1.0000357
## threshold[33]           2.631466e+00  3.052051e+00 2041.8353 0.9996378
## threshold[34]           2.710292e+00  3.185474e+00 3051.1084 0.9992123
## threshold[35]           2.783506e+00  3.286670e+00 2400.3390 0.9994909
## threshold[36]           2.439018e+00  2.791420e+00 1905.5323 0.9992519
## threshold[37]           2.593168e+00  3.197920e+00 2327.8502 0.9996683
## threshold[38]           2.615714e+00  3.133953e+00 2080.9234 1.0001018
## threshold[39]           2.412252e+00  2.773985e+00 2532.9545 1.0002251
## threshold[40]           2.578535e+00  2.894796e+00 1233.1005 0.9998587
## threshold[41]           2.732535e+00  3.221272e+00 2503.8952 0.9992511
## threshold[42]           2.602541e+00  3.188796e+00 2197.5589 0.9995041
## threshold[43]           2.616753e+00  3.112319e+00 2332.8982 1.0007472
## threshold[44]           2.462845e+00  2.838808e+00 2955.1407 0.9998453
## threshold[45]           2.498984e+00  2.969883e+00 3181.8635 1.0009733
## threshold[46]           2.739336e+00  3.293792e+00 2641.8513 0.9998900
## threshold[47]           2.370601e+00  2.669077e+00 2076.3557 1.0004179
## threshold[48]           2.578055e+00  2.890409e+00 1483.7229 0.9994026
## threshold[49]           2.569936e+00  2.857137e+00 1454.9210 0.9999871
## threshold[50]           2.603768e+00  3.327474e+00 1823.7340 0.9996539
## threshold[51]           2.554090e+00  3.032986e+00 2435.8532 0.9997244
## threshold[52]           2.652919e+00  3.275852e+00 2031.6185 1.0013736
## threshold[53]           2.412106e+00  2.716711e+00 2056.6271 0.9995772
## threshold[54]           2.610898e+00  3.113192e+00 1938.0179 0.9990337
## threshold[55]           2.855823e+00  3.386493e+00 1522.5658 1.0011022
## threshold[56]           2.627350e+00  2.975719e+00 1688.2600 1.0010321
## threshold[57]           2.398421e+00  2.740834e+00 2657.0257 0.9999820
## threshold[58]           2.601195e+00  3.091265e+00 2077.6919 0.9997897
## threshold[59]           2.758678e+00  3.458734e+00  816.1415 1.0011721
## threshold[60]           2.672202e+00  3.236752e+00 1151.3115 1.0002990
## threshold[61]           2.689014e+00  3.313972e+00 1641.1103 0.9991768
## threshold[62]           2.523253e+00  2.952345e+00 3305.8114 0.9991100
## threshold[63]           2.608058e+00  3.226076e+00 2043.0677 1.0008503
## threshold[64]           2.652971e+00  3.311422e+00 1071.4996 1.0017964
## threshold[65]           2.660087e+00  3.070807e+00 3283.8387 0.9996953
## threshold[66]           2.732072e+00  3.443637e+00  977.6251 1.0015271
## threshold[67]           2.602273e+00  2.948785e+00 1774.6708 1.0003312
## threshold[68]           2.857367e+00  3.437591e+00 1793.2326 0.9996297
## threshold[69]           2.434725e+00  2.711346e+00 1450.6955 1.0000639
## threshold[70]           2.578507e+00  2.876477e+00 1292.4829 1.0011961
## threshold[71]           2.749613e+00  3.229646e+00 2559.0066 0.9998524
## threshold[72]           2.640758e+00  3.361013e+00 1419.5847 1.0035608
## threshold[73]           2.566797e+00  3.076180e+00 2445.7495 0.9995428
## threshold[74]           2.698730e+00  3.121903e+00 3235.3186 0.9991824
## threshold[75]           2.794581e+00  3.249068e+00 1803.1783 0.9994938
## threshold[76]           2.535448e+00  2.975370e+00 2632.7533 0.9992046
## threshold[77]           2.327094e+00  2.577128e+00  737.8989 0.9993467
## threshold[78]           2.593982e+00  3.050890e+00 3613.8695 0.9991727
## threshold[79]           2.586339e+00  2.899827e+00 1386.1271 1.0006764
## threshold[80]           2.635968e+00  3.173279e+00 2154.3165 0.9993434
## threshold[81]           2.448206e+00  2.859631e+00 3474.7970 0.9996764
## threshold[82]           2.856106e+00  3.512856e+00 1864.3512 0.9997547
## threshold[83]           2.803099e+00  3.292572e+00 2327.1576 0.9991521
## threshold[84]           2.685307e+00  3.055580e+00 2799.2853 1.0000367
## threshold[85]           2.428672e+00  2.699560e+00 1786.7208 0.9995947
## threshold[86]           2.555597e+00  3.022332e+00 2546.3566 1.0001269
## threshold[87]           2.609882e+00  3.170792e+00 2645.1507 0.9992260
## threshold[88]           2.794697e+00  3.295786e+00 2023.5441 1.0009371
## threshold[89]           2.843954e+00  3.444926e+00 1798.3828 1.0011983
## threshold[90]           2.754061e+00  3.484025e+00 1115.4526 1.0015418
## threshold[91]           2.420740e+00  2.684420e+00 1468.4039 0.9995586
## threshold[92]           2.634962e+00  3.250753e+00 1688.7211 0.9993978
## threshold[93]           2.562639e+00  3.069711e+00 3551.6783 0.9991734
## threshold[94]           2.563079e+00  3.127319e+00 2192.8929 0.9994862
## threshold[95]           2.567562e+00  3.098917e+00 2395.8014 1.0020421
## threshold[96]           2.520190e+00  2.982017e+00 2796.1748 1.0005915
## threshold[97]           2.708468e+00  3.208148e+00 2712.3081 0.9993139
## threshold[98]           2.388093e+00  2.685688e+00 2394.5794 0.9996073
## threshold[99]           2.833534e+00  3.467120e+00 2005.3272 0.9999977
## threshold[100]          2.588363e+00  3.077319e+00 2793.6561 1.0000652
## threshold[101]          2.563039e+00  3.149761e+00 2442.4313 1.0003192
## threshold[102]          2.660780e+00  3.067178e+00 2904.8319 0.9994000
## threshold[103]          2.755254e+00  3.378610e+00 2528.5855 0.9993447
## threshold[104]          2.456864e+00  2.858363e+00 2113.0659 0.9997850
## threshold[105]          2.701324e+00  3.157639e+00 3041.8524 0.9998483
## threshold[106]          2.604345e+00  3.168567e+00 2297.6040 0.9994176
## threshold[107]          3.371212e+00  4.547835e+00  357.8662 1.0055432
## threshold[108]          2.497231e+00  2.917602e+00 3212.4128 0.9998340
## threshold[109]          2.527986e+00  2.964049e+00 3321.2473 0.9993015
## threshold[110]          2.600087e+00  3.258328e+00 1646.8583 1.0030415
## threshold[111]          2.589401e+00  3.057919e+00 2753.4111 1.0004457
## threshold[112]          2.571028e+00  3.059327e+00 2054.6682 0.9991933
## threshold[113]          2.442019e+00  2.851866e+00 2961.7448 0.9995253
## threshold[114]          2.529864e+00  3.014890e+00 3147.1983 0.9991864
## threshold[115]          2.476407e+00  2.777468e+00 2770.5647 0.9992391
## threshold[116]          2.562102e+00  3.002557e+00 3425.3484 1.0003594
## threshold[117]          2.839088e+00  3.417349e+00 1818.9773 1.0004253
## threshold[118]          2.573940e+00  3.171108e+00 2765.1458 0.9995900
## threshold[119]          2.671436e+00  3.223625e+00 1426.9726 1.0003983
## threshold[120]          2.534144e+00  2.966314e+00 3251.7820 0.9994242
## threshold[121]          2.552421e+00  3.006369e+00 2344.9531 0.9992082
## threshold[122]          2.516899e+00  2.881171e+00 4061.5588 0.9992964
## threshold[123]          2.539130e+00  2.975546e+00 3525.5707 0.9990295
## threshold[124]          2.671502e+00  3.208700e+00 1438.1692 1.0009428
## threshold[125]          2.882744e+00  3.422145e+00 1720.1487 1.0001270
## threshold[126]          2.632380e+00  3.196899e+00 2535.5578 1.0004049
## threshold[127]          2.695362e+00  3.318542e+00  984.0626 1.0014504
## threshold[128]          2.530104e+00  3.015592e+00 2862.8715 1.0008397
## threshold[129]          2.407181e+00  2.710129e+00 1445.3164 1.0002681
## threshold[130]          2.853264e+00  3.466880e+00 1502.0021 1.0004765
## threshold[131]          2.709242e+00  3.130839e+00 2728.2793 0.9993353
## threshold[132]          2.621586e+00  3.220069e+00 1985.3092 0.9996837
## threshold[133]          2.506763e+00  2.928502e+00 3294.4780 0.9991778
## threshold[134]          2.651686e+00  3.208128e+00 1602.7203 1.0034303
## threshold[135]          2.549509e+00  3.110420e+00 3126.3575 0.9990353
## threshold[136]          2.676494e+00  3.331231e+00 1689.8452 1.0007113
## threshold[137]          2.682318e+00  3.064030e+00 2962.8306 0.9995535
## threshold[138]          2.818860e+00  3.325315e+00 2126.1656 0.9997264
## threshold[139]          2.737672e+00  3.387981e+00 1290.6651 1.0024262
## threshold[140]          2.504232e+00  2.915532e+00 3305.9059 0.9996130
## threshold[141]          2.556883e+00  3.014547e+00 2355.1970 0.9990943
## threshold[142]          2.823697e+00  3.404557e+00 2404.7735 1.0001627
## threshold[143]          2.596296e+00  3.026222e+00 3023.2360 0.9997978
## threshold[144]          2.598632e+00  3.102375e+00 2232.6155 0.9991226
## threshold[145]          2.535970e+00  3.049344e+00 2277.3689 0.9999304
## threshold[146]          2.641247e+00  3.169286e+00 2180.7794 1.0004548
## threshold[147]          2.291806e+00  2.583944e+00  735.6180 1.0003816
## threshold[148]          2.757933e+00  3.320042e+00 2895.9448 1.0009061
## threshold[149]          2.615801e+00  2.975590e+00 2143.6118 0.9991712
## threshold[150]          2.510461e+00  2.910528e+00 3238.2199 0.9994523
## spread[1]               2.091256e+00  3.292970e+00 1032.8268 1.0021629
## spread[2]               2.108063e+00  2.797122e+00 1250.4003 1.0055875
## spread[3]               1.938444e+00  2.668543e+00 1411.7630 1.0027850
## spread[4]               2.448625e+00  3.140414e+00 1373.5191 0.9998426
## spread[5]               2.437217e+00  3.333859e+00 1343.3470 1.0021674
## spread[6]               1.519953e+00  2.037450e+00 2186.3206 1.0005035
## spread[7]               2.114382e+00  2.795679e+00 1654.6318 1.0016032
## spread[8]               2.536425e+00  3.661368e+00  591.3533 1.0093142
## spread[9]               1.445857e+00  1.873883e+00 1233.3808 1.0029599
## spread[10]              2.367100e+00  3.473141e+00  555.5563 1.0011096
## spread[11]              1.885015e+00  2.585687e+00 1835.4171 0.9995158
## spread[12]              1.873518e+00  2.445918e+00 2456.0501 1.0001250
## spread[13]              1.589940e+00  2.096649e+00 2964.0646 0.9993938
## spread[14]              2.154211e+00  3.252486e+00 1851.5256 1.0005582
## spread[15]              2.269159e+00  3.052610e+00  805.1930 1.0063682
## spread[16]              1.709676e+00  2.268945e+00 2501.4676 0.9998379
## spread[17]              1.911864e+00  2.516584e+00 2372.3588 0.9995961
## spread[18]              1.563009e+00  2.029378e+00 2535.0124 0.9991874
## spread[19]              1.861189e+00  2.825815e+00 1994.5433 1.0001495
## spread[20]              1.778087e+00  2.312988e+00 2898.5226 1.0003119
## spread[21]              2.307407e+00  2.974228e+00 1794.8950 1.0019420
## spread[22]              1.935484e+00  2.469795e+00 3193.9511 0.9991110
## spread[23]              1.982426e+00  2.599777e+00 1709.0577 1.0017934
## spread[24]              1.886264e+00  2.815313e+00 2635.3659 1.0009610
## spread[25]              2.226557e+00  3.081131e+00  971.2226 1.0047735
## spread[26]              2.397916e+00  3.310233e+00 1197.0495 1.0011288
## spread[27]              1.676947e+00  2.190479e+00 2409.2438 0.9992238
## spread[28]              2.098397e+00  2.731909e+00 1763.6457 0.9996415
## spread[29]              1.894920e+00  2.432758e+00 1745.3150 1.0028746
## spread[30]              2.379670e+00  3.816483e+00  412.2333 1.0099141
## spread[31]              1.628584e+00  2.103440e+00 2559.6486 0.9992077
## spread[32]              2.033042e+00  3.453575e+00  699.1315 1.0076425
## spread[33]              1.960266e+00  2.534175e+00 2350.9115 1.0026945
## spread[34]              1.826526e+00  2.370852e+00 2674.9784 0.9994933
## spread[35]              1.746240e+00  2.304454e+00 3077.1450 0.9992160
## spread[36]              1.790187e+00  2.324130e+00 2787.8339 1.0000959
## spread[37]              2.173028e+00  3.424451e+00  864.2456 1.0032139
## spread[38]              1.930890e+00  2.617925e+00 2055.5797 1.0013086
## spread[39]              2.167666e+00  2.939013e+00 2282.8659 1.0009759
## spread[40]              1.482450e+00  1.946989e+00 1556.4634 1.0006555
## spread[41]              1.811609e+00  2.453597e+00 2197.7237 0.9998679
## spread[42]              2.303876e+00  3.554724e+00 1228.6814 1.0000335
## spread[43]              2.165724e+00  3.171483e+00  809.9125 1.0013721
## spread[44]              1.775732e+00  2.307044e+00 3191.0949 0.9994419
## spread[45]              1.903312e+00  2.447729e+00 2857.7821 0.9996139
## spread[46]              1.856956e+00  2.745228e+00 2397.9393 0.9996383
## spread[47]              1.559157e+00  2.136664e+00 1563.3461 1.0013958
## spread[48]              1.639189e+00  2.230489e+00 2730.0635 1.0001423
## spread[49]              1.543792e+00  1.958143e+00 2850.3329 0.9990216
## spread[50]              2.450206e+00  3.722047e+00 1277.8338 1.0012592
## spread[51]              2.445551e+00  3.189681e+00 1084.1074 1.0064335
## spread[52]              2.222769e+00  2.944704e+00 1400.1693 1.0002922
## spread[53]              1.768573e+00  2.286124e+00 2493.5997 0.9996838
## spread[54]              1.983307e+00  2.622958e+00 2254.9063 0.9993128
## spread[55]              1.792516e+00  2.298579e+00 2378.6170 0.9993784
## spread[56]              1.465752e+00  1.963576e+00 2080.4305 1.0013638
## spread[57]              1.774796e+00  2.329371e+00 2671.1082 0.9995165
## spread[58]              1.774322e+00  2.254568e+00 2252.9410 0.9998005
## spread[59]              2.391155e+00  3.123754e+00 1251.4875 1.0001287
## spread[60]              2.428111e+00  3.331489e+00 1443.3377 1.0006090
## spread[61]              2.232093e+00  2.898696e+00 2157.1124 1.0004330
## spread[62]              1.945844e+00  2.610597e+00 2188.2841 1.0004536
## spread[63]              2.425834e+00  3.261418e+00 1299.2627 1.0005164
## spread[64]              2.506179e+00  3.439060e+00  780.5810 1.0061172
## spread[65]              2.059772e+00  2.642683e+00 2231.6816 1.0011342
## spread[66]              2.288706e+00  3.024362e+00 1820.7142 1.0005370
## spread[67]              1.518524e+00  1.989446e+00 2084.5932 1.0006779
## spread[68]              1.916847e+00  2.861837e+00 1134.1167 0.9996626
## spread[69]              1.311154e+00  1.716120e+00 1252.8621 1.0021308
## spread[70]              1.814103e+00  2.371970e+00 2629.6447 0.9994589
## spread[71]              2.108856e+00  2.801444e+00 1791.0256 1.0009942
## spread[72]              2.108450e+00  3.155000e+00 1218.1045 1.0038933
## spread[73]              2.199867e+00  2.913223e+00 1642.0453 1.0028505
## spread[74]              1.785744e+00  2.371002e+00 2498.7579 0.9993171
## spread[75]              1.899353e+00  2.469460e+00 2373.9745 1.0006456
## spread[76]              1.940064e+00  2.635991e+00 1395.2634 1.0011971
## spread[77]              1.224756e+00  1.668102e+00  720.3936 1.0018025
## spread[78]              1.671988e+00  2.181012e+00 2851.7711 0.9996378
## spread[79]              1.914707e+00  2.472912e+00 2474.8816 0.9992153
## spread[80]              2.324015e+00  3.205422e+00 1545.8691 0.9997883
## spread[81]              2.202256e+00  3.007402e+00 2002.5500 0.9995153
## spread[82]              2.035280e+00  2.718364e+00 2130.8291 1.0001797
## spread[83]              1.709632e+00  2.234843e+00 2639.3953 1.0000397
## spread[84]              1.422825e+00  1.896951e+00 1798.0537 1.0012787
## spread[85]              1.427428e+00  1.902374e+00 1725.0933 0.9992004
## spread[86]              2.000934e+00  3.110510e+00  676.9056 0.9992055
## spread[87]              2.099452e+00  3.396870e+00  460.6772 1.0058745
## spread[88]              1.940896e+00  2.515044e+00 2352.8905 1.0000590
## spread[89]              2.061099e+00  2.899608e+00 1432.4715 1.0010980
## spread[90]              2.407045e+00  3.235547e+00  780.2179 1.0035827
## spread[91]              1.555395e+00  2.097821e+00 3193.8119 0.9992161
## spread[92]              2.243984e+00  2.969862e+00 2194.6376 1.0010696
## spread[93]              2.176111e+00  3.206344e+00  468.7492 1.0022979
## spread[94]              2.193789e+00  3.479370e+00 1352.2492 1.0001146
## spread[95]              1.958899e+00  2.518934e+00 2274.6648 0.9998410
## spread[96]              1.973706e+00  3.425992e+00  551.5403 1.0054626
## spread[97]              1.967841e+00  2.884412e+00 2245.0584 1.0003797
## spread[98]              1.654385e+00  2.175192e+00 1666.5537 0.9999262
## spread[99]              2.125307e+00  2.747544e+00 1519.4772 1.0030588
## spread[100]             1.986394e+00  2.569672e+00 2020.3014 1.0008943
## spread[101]             2.827704e+00  3.968658e+00  727.6259 1.0058231
## spread[102]             1.644970e+00  2.202056e+00 2737.4524 0.9994356
## spread[103]             1.946529e+00  2.902187e+00 1945.1400 1.0044765
## spread[104]             1.989926e+00  2.610496e+00 2501.9328 0.9995088
## spread[105]             1.797616e+00  2.361668e+00 2616.3223 0.9998272
## spread[106]             2.433102e+00  3.361475e+00 1127.6969 1.0012301
## spread[107]             2.258941e+00  3.027063e+00  621.2811 1.0031291
## spread[108]             2.103102e+00  2.741052e+00 2863.6420 0.9994492
## spread[109]             1.823360e+00  2.342359e+00 2792.2554 0.9996604
## spread[110]             2.482009e+00  4.104011e+00  530.8039 1.0026774
## spread[111]             1.719125e+00  2.224597e+00 2355.5237 1.0004666
## spread[112]             1.969845e+00  2.542693e+00 3004.9623 0.9999533
## spread[113]             1.867545e+00  2.469441e+00 2852.9102 0.9994708
## spread[114]             2.101288e+00  3.354226e+00  637.1554 0.9997870
## spread[115]             1.793384e+00  2.374124e+00 2502.1728 0.9992525
## spread[116]             1.716652e+00  2.277445e+00 2651.1052 1.0004758
## spread[117]             1.968968e+00  2.654410e+00 1684.6062 1.0040407
## spread[118]             2.059027e+00  3.210128e+00 1046.3790 1.0068669
## spread[119]             1.906029e+00  2.463406e+00 2798.0623 0.9996273
## spread[120]             2.145094e+00  2.807829e+00 1290.2593 1.0007344
## spread[121]             1.906134e+00  2.487856e+00 2718.3708 1.0007434
## spread[122]             1.507407e+00  1.949011e+00 3367.9209 1.0007484
## spread[123]             1.718148e+00  2.222491e+00 2482.1738 0.9996612
## spread[124]             2.002197e+00  2.578404e+00 2160.3542 1.0000877
## spread[125]             1.772665e+00  2.295941e+00 2505.8205 0.9996161
## spread[126]             2.071765e+00  2.910143e+00 1046.8661 1.0018889
## spread[127]             2.229066e+00  2.933777e+00 1096.5542 1.0017725
## spread[128]             1.811528e+00  2.699480e+00  720.6177 1.0035855
## spread[129]             1.547669e+00  2.051532e+00 2191.5911 0.9992870
## spread[130]             2.087061e+00  2.683448e+00 1298.5338 1.0052440
## spread[131]             1.538718e+00  2.004647e+00 2450.2075 0.9994543
## spread[132]             2.428947e+00  3.696448e+00  787.7916 1.0084238
## spread[133]             1.877512e+00  2.538874e+00 3184.5503 0.9993704
## spread[134]             1.979071e+00  2.534487e+00 2035.2196 0.9995148
## spread[135]             2.133282e+00  3.109111e+00 2108.9265 0.9998098
## spread[136]             2.285736e+00  2.929150e+00 1021.5009 1.0014028
## spread[137]             1.618213e+00  2.101966e+00 3147.5155 1.0003672
## spread[138]             1.721884e+00  2.202254e+00 2477.4604 0.9992743
## spread[139]             1.991691e+00  2.548507e+00 1039.3299 1.0008869
## spread[140]             1.599578e+00  2.070714e+00 3472.7173 0.9994940
## spread[141]             2.389982e+00  3.196683e+00 1936.8624 1.0001537
## spread[142]             1.821796e+00  2.635222e+00 1417.0526 0.9995378
## spread[143]             1.675681e+00  2.185850e+00 2681.1851 0.9999541
## spread[144]             2.192116e+00  2.871361e+00 2300.5034 1.0002249
## spread[145]             2.391440e+00  3.532803e+00  667.9968 1.0075889
## spread[146]             1.990854e+00  2.907962e+00  946.1955 1.0006642
## spread[147]             1.488356e+00  2.030472e+00 1188.4441 1.0020020
## spread[148]             2.012757e+00  2.968069e+00 1250.9286 1.0004145
## spread[149]             1.581874e+00  2.015731e+00 2598.1468 0.9992486
## spread[150]             1.636741e+00  2.136265e+00 2317.3695 0.9997099
## lapse[1]                1.306733e-01  1.829313e-01 1336.9670 1.0000008
## lapse[2]                2.597972e-02  7.365492e-02 1789.4989 0.9998359
## lapse[3]                2.725629e-02  6.484364e-02 2410.5355 1.0005639
## lapse[4]                1.900084e-02  6.450618e-02 1627.4720 1.0001495
## lapse[5]                4.394883e-02  9.065681e-02 1576.1615 1.0010099
## lapse[6]                8.413888e-03  3.202587e-02 2109.6577 0.9996194
## lapse[7]                2.022813e-02  6.467083e-02 1943.0725 0.9991563
## lapse[8]                6.765096e-02  1.191118e-01  851.4266 1.0076521
## lapse[9]                8.086989e-03  2.878117e-02 2357.1961 0.9993980
## lapse[10]               7.156767e-02  1.210161e-01  755.9048 1.0005435
## lapse[11]               3.318444e-02  7.637457e-02 2250.6211 0.9993979
## lapse[12]               1.186142e-02  3.963372e-02 2444.9713 0.9998622
## lapse[13]               8.070929e-03  2.937554e-02 2657.0686 1.0000792
## lapse[14]               2.026606e-01  2.590585e-01 2260.1528 0.9995327
## lapse[15]               4.904380e-02  1.098295e-01 1108.7386 1.0033297
## lapse[16]               9.427218e-03  3.187649e-02 2790.6002 0.9996718
## lapse[17]               1.657200e-02  4.643353e-02 2024.1190 1.0008459
## lapse[18]               8.585532e-03  2.904048e-02 2303.6803 1.0004851
## lapse[19]               3.348241e-01  3.937101e-01 2333.6067 0.9993624
## lapse[20]               1.095499e-02  4.041538e-02 1910.8133 0.9991397
## lapse[21]               1.886410e-02  6.574493e-02 1958.2315 1.0004737
## lapse[22]               9.696101e-03  3.419960e-02 2155.4698 1.0005924
## lapse[23]               1.902579e-02  6.054842e-02 2178.4552 0.9994775
## lapse[24]               4.101154e-01  4.684987e-01 2115.0178 0.9996026
## lapse[25]               5.252185e-02  1.075015e-01 1638.3416 1.0013636
## lapse[26]               6.547302e-02  1.166194e-01 1306.2463 0.9996846
## lapse[27]               9.485821e-03  3.392281e-02 2575.1381 0.9992911
## lapse[28]               2.528469e-02  7.119885e-02 1733.0123 1.0001266
## lapse[29]               1.238182e-02  4.965500e-02 1871.3700 0.9993275
## lapse[30]               1.211008e-01  1.777747e-01  644.2350 1.0022372
## lapse[31]               8.529003e-03  3.241058e-02 2083.4326 0.9999407
## lapse[32]               1.297305e-01  1.866207e-01 1360.6846 1.0009567
## lapse[33]               1.272136e-02  4.443849e-02 2600.3208 0.9995981
## lapse[34]               1.454504e-02  4.701149e-02 2585.1064 0.9991804
## lapse[35]               1.351231e-02  4.589627e-02 2320.6478 0.9995442
## lapse[36]               9.395520e-03  3.718692e-02 2467.7871 0.9991716
## lapse[37]               1.515682e-01  2.109238e-01 1541.5763 1.0001830
## lapse[38]               1.336594e-02  4.530045e-02 2964.6594 0.9991288
## lapse[39]               1.359106e-02  4.234216e-02 2119.3634 0.9999557
## lapse[40]               7.338186e-03  2.618109e-02 2696.2988 0.9997053
## lapse[41]               2.691935e-02  6.577189e-02 1780.6803 1.0011045
## lapse[42]               2.371388e-01  2.966877e-01 2846.0682 0.9997927
## lapse[43]               6.381972e-02  1.172359e-01 1453.3096 0.9997503
## lapse[44]               9.592900e-03  4.011907e-02 2370.8166 0.9990692
## lapse[45]               1.162701e-02  3.909942e-02 1963.7346 0.9993605
## lapse[46]               3.903824e-01  4.526265e-01 1827.6823 0.9990971
## lapse[47]               7.953277e-03  2.777476e-02 1944.3800 1.0002088
## lapse[48]               8.782371e-03  3.406692e-02 2407.1764 1.0009395
## lapse[49]               8.001736e-03  3.229472e-02 1689.8887 1.0010547
## lapse[50]               2.310614e-01  2.871781e-01 2360.2582 1.0030306
## lapse[51]               2.735119e-02  7.389757e-02 1697.3317 1.0025351
## lapse[52]               2.260739e-02  6.663573e-02 1821.6087 0.9995603
## lapse[53]               1.224468e-02  3.966896e-02 2594.6054 0.9997614
## lapse[54]               1.542648e-02  4.888922e-02 2192.7981 1.0012820
## lapse[55]               1.103492e-02  3.931568e-02 1915.0265 1.0021659
## lapse[56]               7.617517e-03  2.500689e-02 2416.8661 1.0003895
## lapse[57]               8.737833e-03  3.261477e-02 2385.7167 1.0000202
## lapse[58]               1.139664e-02  4.152090e-02 1968.6743 0.9993593
## lapse[59]               2.090250e-02  6.703767e-02 1924.7120 0.9994392
## lapse[60]               5.232029e-02  1.062564e-01 1556.1429 1.0000069
## lapse[61]               1.550560e-02  5.866156e-02 2347.9306 1.0003352
## lapse[62]               2.907914e-02  6.673367e-02 2376.6743 1.0002002
## lapse[63]               3.083239e-02  8.304891e-02 1580.8590 1.0004604
## lapse[64]               4.204405e-02  1.002478e-01 1602.7591 1.0014524
## lapse[65]               1.126542e-02  4.570297e-02 2059.6829 1.0004150
## lapse[66]               2.913593e-02  7.920719e-02 1733.9672 1.0010125
## lapse[67]               7.866089e-03  3.142476e-02 1935.7278 0.9993167
## lapse[68]               6.943417e-02  1.178143e-01 1201.8538 1.0003621
## lapse[69]               6.580680e-03  2.361638e-02 2208.9556 1.0003928
## lapse[70]               1.246323e-02  4.283114e-02 2396.1376 1.0000020
## lapse[71]               3.545404e-02  8.407553e-02 1643.6045 1.0026159
## lapse[72]               2.257772e-01  2.872763e-01 2179.6557 1.0000056
## lapse[73]               3.098259e-02  7.129652e-02 2014.5427 1.0031994
## lapse[74]               1.023450e-02  3.600629e-02 2220.9631 0.9992715
## lapse[75]               1.157068e-02  4.662276e-02 2223.0429 0.9994408
## lapse[76]               3.500680e-02  7.714779e-02 1745.2992 0.9994818
## lapse[77]               6.078820e-03  2.073885e-02 2411.5873 1.0005235
## lapse[78]               8.880078e-03  3.191242e-02 2265.5458 1.0004752
## lapse[79]               1.374942e-02  4.137048e-02 2555.1262 0.9992591
## lapse[80]               4.789763e-02  9.680647e-02 1820.5480 1.0005952
## lapse[81]               2.544054e-02  6.249568e-02 2868.6139 1.0007040
## lapse[82]               2.078648e-02  6.491193e-02 2024.2861 0.9995666
## lapse[83]               9.476246e-03  3.145906e-02 1940.2226 0.9994865
## lapse[84]               8.599853e-03  3.075256e-02 2544.1248 0.9993332
## lapse[85]               6.783485e-03  2.482402e-02 2643.5282 1.0002263
## lapse[86]               1.076400e-01  1.668412e-01 1346.3506 0.9991471
## lapse[87]               1.010301e-01  1.551526e-01  773.9607 1.0033575
## lapse[88]               1.725983e-02  5.625906e-02 2012.5978 1.0004885
## lapse[89]               5.398707e-02  1.027882e-01 1694.0654 0.9990752
## lapse[90]               3.610571e-02  9.081934e-02 1252.6438 1.0001068
## lapse[91]               7.878511e-03  3.063342e-02 2369.1191 1.0003887
## lapse[92]               2.136021e-02  6.125456e-02 1913.7871 1.0000428
## lapse[93]               6.701870e-02  1.181408e-01 1263.5239 0.9992312
## lapse[94]               2.332105e-01  2.875086e-01 2178.8437 0.9995868
## lapse[95]               1.076687e-02  4.291524e-02 2019.2540 1.0001652
## lapse[96]               1.093419e-01  1.563881e-01  803.1449 1.0015874
## lapse[97]               3.340653e-01  3.970719e-01 2339.7456 1.0002448
## lapse[98]               8.579994e-03  3.302224e-02 1983.0569 1.0014202
## lapse[99]               2.457877e-02  7.311079e-02 1896.7274 0.9997830
## lapse[100]              1.234881e-02  4.467156e-02 2659.6550 0.9996572
## lapse[101]              6.186530e-02  1.207391e-01 1154.3834 1.0038768
## lapse[102]              8.781108e-03  3.605555e-02 2386.3703 1.0025265
## lapse[103]              2.319012e-01  2.876745e-01 2432.8923 1.0004136
## lapse[104]              1.474412e-02  4.613940e-02 2744.5548 0.9997869
## lapse[105]              1.481267e-02  5.055754e-02 2188.8855 0.9999175
## lapse[106]              4.169837e-02  8.958701e-02 1637.3010 0.9999462
## lapse[107]              2.519174e-02  8.466716e-02 1881.2092 1.0006961
## lapse[108]              1.351156e-02  4.411959e-02 2288.2028 1.0005629
## lapse[109]              9.514449e-03  3.867353e-02 2094.9450 0.9997213
## lapse[110]              1.512401e-01  2.086770e-01  816.3788 1.0013415
## lapse[111]              9.049904e-03  3.660203e-02 2188.7798 0.9994037
## lapse[112]              1.203926e-02  4.385493e-02 2391.7493 0.9990963
## lapse[113]              1.077365e-02  3.851109e-02 2471.1380 1.0016121
## lapse[114]              1.048115e-01  1.585819e-01 1043.1837 1.0007530
## lapse[115]              8.664524e-03  3.169345e-02 2228.1004 0.9999167
## lapse[116]              9.676606e-03  3.801433e-02 2038.6504 0.9998107
## lapse[117]              3.692002e-02  8.871113e-02 2666.2466 0.9999918
## lapse[118]              1.549300e-01  2.111683e-01 1629.2493 1.0015103
## lapse[119]              1.182059e-02  4.285832e-02 2483.8628 0.9990738
## lapse[120]              1.100653e-02  4.075206e-02 2184.6115 0.9996759
## lapse[121]              1.037410e-02  3.431290e-02 2321.4963 1.0003673
## lapse[122]              8.345601e-03  2.947357e-02 2052.1189 1.0003969
## lapse[123]              9.554876e-03  3.738375e-02 2066.4911 0.9991736
## lapse[124]              1.156116e-02  4.239183e-02 2159.4257 0.9992690
## lapse[125]              1.131485e-02  4.539440e-02 1803.0135 0.9991031
## lapse[126]              5.216009e-02  1.011517e-01 1545.9450 1.0003623
## lapse[127]              3.402383e-02  8.179496e-02 1858.5275 1.0021039
## lapse[128]              1.626392e-01  2.165842e-01 1590.9595 1.0006571
## lapse[129]              6.862606e-03  2.676027e-02 1704.7847 0.9993275
## lapse[130]              2.602126e-02  7.427420e-02 2227.4424 1.0011784
## lapse[131]              1.053272e-02  3.371309e-02 2607.0319 1.0010286
## lapse[132]              8.855351e-02  1.410589e-01 1124.6297 1.0040961
## lapse[133]              1.157867e-02  4.135387e-02 1994.7461 1.0001609
## lapse[134]              1.261194e-02  5.129086e-02 1765.4204 1.0018868
## lapse[135]              3.621481e-01  4.241578e-01 2260.0714 0.9991660
## lapse[136]              1.561599e-02  5.860605e-02 2022.6141 0.9991864
## lapse[137]              1.043554e-02  3.691503e-02 2840.8225 1.0003822
## lapse[138]              1.129318e-02  4.202772e-02 2149.6459 1.0001958
## lapse[139]              1.472484e-02  5.206409e-02 1745.3948 0.9996027
## lapse[140]              7.854653e-03  3.201372e-02 2170.0469 1.0006414
## lapse[141]              2.588718e-02  7.963258e-02 1877.3937 0.9997856
## lapse[142]              5.890168e-02  1.007376e-01 1735.7335 0.9996071
## lapse[143]              9.008318e-03  3.241437e-02 2351.9247 1.0007868
## lapse[144]              2.927654e-02  7.886734e-02 2507.7714 1.0005562
## lapse[145]              8.445135e-02  1.357798e-01 1161.1911 1.0057818
## lapse[146]              4.593606e-02  9.322727e-02 1674.3422 1.0004514
## lapse[147]              7.740642e-03  2.727839e-02 2529.6627 0.9994264
## lapse[148]              6.222816e-02  1.152879e-01 2042.1526 1.0000591
## lapse[149]              9.361445e-03  3.521017e-02 2513.4999 0.9997966
## lapse[150]              8.591128e-03  3.100890e-02 2066.6446 0.9996821
## lp__                   -6.474674e+03 -6.451897e+03  562.8472 1.0001156

Results

Let’s take a look at our parameter estimates. Here’s the standard way to do this

plot(mdl,pars=c('b_threshold[1]','b_spread[1]','b_lapse[1]','b_threshold[2]','b_spread[2]','b_lapse[2]','b_threshold[3]','b_spread[3]','b_lapse[3]','sigma_log_threshold','sigma_log_spread','sigma_logit_lapse','threshold[1]','spread[1]','lapse[1]'))
## ci_level: 0.8 (80% intervals)
## outer_level: 0.95 (95% intervals)

There are some problems with this view. The parameter names for the condition means are indices into the vectors b_threshold, b_spread, and b_lapse, so these parameters are hard to interpret. Further, these hyperparameters for effects of visualization condition on the mean of each PF parameter are in a transformed parameter space. Their raw values are not very meaningful. What we need to do is recover meaningful parameter names and plug posterior samples into our model to generate possible estimated psychometric functions.

PFs for individuals

Getting the posterior

First, we need to recover our condition names from the numeric indices in our model. Thankfully, tidybayes will do this for us.

mdl %<>% recover_types(useData)

Next, we’ll want to pull our posterior samples of individual PF parameter estimates into a tidy (i.e., long) data table.

# assign posterior samples to tidy tibble
post <- mdl %>% # should reduce to used params only
  spread_draws(threshold[subject],spread[subject],lapse[subject])
# print table
post
## # A tibble: 300,000 x 7
## # Groups:   subject [150]
##    .chain .iteration .draw subject threshold spread    lapse
##     <int>      <int> <int> <fct>       <dbl>  <dbl>    <dbl>
##  1      1          1     1 1            2.46   1.58 0.154   
##  2      1          1     1 2            2.48   1.46 0.0354  
##  3      1          1     1 3            2.39   1.25 0.0246  
##  4      1          1     1 4            2.38   2.06 0.0107  
##  5      1          1     1 5            2.43   1.98 0.0128  
##  6      1          1     1 6            2.37   1.20 0.00136 
##  7      1          1     1 7            2.26   1.34 0.0152  
##  8      1          1     1 8            2.16   1.62 0.0571  
##  9      1          1     1 9            2.58   1.38 0.000365
## 10      1          1     1 10           2.43   1.49 0.0635  
## # ... with 299,990 more rows

Subset the posterior

Let’s look at only 100 (approximatedly equally likely) draws from our posterior, just to keep the amount of data we are processing and visualizing reasonable.

post_small = 
  post %>%
  filter(.draw %in% floor(seq(1, 2000, length.out = 100)))

Make a prediction grid

We’ll want to plot PFs for each subject across the range of intensity values observed. Since we can only plot so many subjects simultaneously in one view, we’ll make predictions for only a subset of subjects in this illustration.

n_intensity <- 101
intensity <- seq_range(useData$intensity, n = n_intensity)

grid = useData %>% 
  data_grid(nesting(condition, subject)) %>%
  filter(as.numeric(subject) %in% 1:27) %>%
  mutate(intensity = list(intensity))

grid
## # A tibble: 27 x 3
##    condition subject intensity  
##    <fct>     <fct>   <list>     
##  1 c         1       <dbl [101]>
##  2 c         9       <dbl [101]>
##  3 c         13      <dbl [101]>
##  4 c         18      <dbl [101]>
##  5 c         19      <dbl [101]>
##  6 c         20      <dbl [101]>
##  7 c         24      <dbl [101]>
##  8 c         25      <dbl [101]>
##  9 c         27      <dbl [101]>
## 10 h         2       <dbl [101]>
## # ... with 17 more rows

Run the psychometric function over the prediction grid

Here, we call the psychometric function we defined above for each subject * draw from our posterior.

pfdf = grid %>%
  inner_join(post_small) %>%
  mutate(pf = pmap(list(intensity, threshold, spread, lapse), ~  psychometric(..1, ..2, ..3, 0.5, ..4))) %>%
  unnest()
## Joining, by = "subject"

Plot the PF

Here, we create hypothetical outcome plots showing estimated psychometric functions for each draw from our posterior distribution of parameter estimates.

p = pfdf %>%
  group_by(condition) %>%
  mutate(subject = as.numeric(factor(subject))) %>%
  filter(subject %in% 1:3) %>%
  ggplot(aes(intensity, pf)) +
  theme_minimal() +
  geom_line() +
  facet_grid(subject ~ condition, scales = "free") +
  transition_manual(.draw)

animate(p, fps=2.5, width=500, height=300)

PFs for average individual in each condition

Getting the posterior

Next, we’ll want to pull our posterior samples of the population mean PF parameters into a tidy (i.e., long) data table.

# assign posterior samples to tidy tibble
post_avg <- mdl %>% # should reduce to used params only
  spread_draws(b_threshold[condition],b_spread[condition],b_lapse[condition])
# print table
post_avg
## # A tibble: 6,000 x 7
## # Groups:   condition [3]
##    .chain .iteration .draw condition b_threshold b_spread b_lapse
##     <int>      <int> <int> <fct>           <dbl>    <dbl>   <dbl>
##  1      1          1     1 c               0.954    0.427   -3.97
##  2      1          1     1 h               0.880    0.456   -4.31
##  3      1          1     1 hf              0.803    0.526   -4.96
##  4      1          2     2 c               0.992    0.482   -4.03
##  5      1          2     2 h               0.874    0.393   -4.32
##  6      1          2     2 hf              0.820    0.594   -4.61
##  7      1          3     3 c               0.862    0.508   -4.12
##  8      1          3     3 h               0.797    0.506   -4.67
##  9      1          3     3 hf              0.927    0.615   -3.86
## 10      1          4     4 c               0.834    0.504   -4.33
## # ... with 5,990 more rows

Subset the posterior

Let’s look at only 100 (approximatedly equally likely) draws from our posterior, just to keep the amount of data we are processing and visualizing reasonable.

post_small_avg = 
  post_avg %>%
  filter(.draw %in% floor(seq(1, 2000, length.out = 100)))

Make a prediction grid

We’ll want to plot PFs across the range of intensity values observed. We’ll plot the average PF for each condition in our experiment.

n_intensity <- 101
intensity <- seq_range(useData$intensity, n = n_intensity)

grid = useData %>% 
  data_grid(condition) %>%
  mutate(intensity = list(intensity))

grid
## # A tibble: 3 x 2
##   condition intensity  
##   <fct>     <list>     
## 1 c         <dbl [101]>
## 2 h         <dbl [101]>
## 3 hf        <dbl [101]>

Run the psychometric function over the prediction grid

Here, we call the psychometric function we defined above for each condition * draw from our posterior.

# this time we need to transform the parameters since these are our hyperparameters
pfdf_avg = grid %>%
  inner_join(post_small_avg) %>%
  mutate(pf = pmap(list(intensity, exp(b_threshold), exp(b_spread), plogis(b_lapse)), ~  psychometric(..1, ..2, ..3, 0.5, ..4))) %>%
  unnest()
## Joining, by = "condition"

Plot the PF

Here, we create hypothetical outcome plots showing estimated psychometric functions for each draw from our posterior distribution of parameter estimates.

p = pfdf_avg %>%
  group_by(condition) %>%
  ggplot(aes(intensity, pf)) +
  theme_minimal() +
  geom_line() +
  facet_grid(~ condition, scales = "free") +
  transition_manual(.draw)

animate(p, fps=2.5, width=500, height=200)

Here’s the same plot using color rather than facting to differentiate conditions.

p = pfdf_avg %>%
  group_by(condition) %>%
  ggplot(aes(intensity, pf, color=condition)) +
  theme_minimal() +
  geom_line() +
  transition_manual(.draw)

animate(p, fps=2.5, width=500, height=200)